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Book ,~p: 


PRESENTED HY 














ELEMENTS 


V3M 

OF 

SURVEYIN G, 


AND 

NAVIGATION, 


WITH DESCRIPTIONS OF THE INSTRUMENTS AND THE 

NECESSARY TABLES. 


BY CHARLES DAVIES, LL. D., 

AUTHOR OF ARITHMETIC, ALGEBRA, PRACTICAL MATHEMATICS FOR PRACTICAL MEN^ 
ELEMENTS OF DESCRIPTIVE GEOMETRY, SHADES, SHADOWS, AND PER¬ 
SPECTIVE, ANALYTICAL GEOMETRY, DIFFERENTIAL AND 
INTEGRAL CALCULUS. 


REVISED EDITION. 


HEVT YORK: 

PUBLISHED BY A. S. BARNES & CO., 
No. 51 JOIIN-STREET. 
CINCINNATI: H. W. DERBY & CO., 

»» 



DAVIES’ 

COURSE OE MATHEMATICS. 


Babies’ jflvst Wessons lit Slrltljmctlc—For Beginners. 

babies’ gtatbmetlc—Designed for the use of Academies and Schools. 

men to Babies’ &rtt$mettc. 

Babies’ Saulbersltp Sln'tijmetic—Embracing the Science of Numbers and their 
numerous Applications. 

3&ep to Babies’ SKtilbersltp Stvltijmetle. 

Babies’ JSlemcntavp SUgcbra—Being an introduction to the Science, and form¬ 
ing a connecting link between Arithmetic and Algebra. 

o o 

2&e» to Babies’ Blcweiitarn Algebra. 

Babies’ Elements of (£eometro and 2Trlgoitometrp, with Applications in 
Mensuration.— This work embraces the elementary principles of Geometry and 
Trigonometry. The reasoning is plain and concise, but at the same time strictly 
rigorous. 

Babies’ practical |Uatl)emattcs for practical iftsleti—Embracing the Princi¬ 
ples of Drawing, Architecture, Mensuration, and Logarithms, with Applications 
to the Mechanic Arts. 

Babies’ 33ourtron’S Silgefcra—Including Sturm’s Theorem —Being an abridg¬ 
ment of the Work of M. Bourdon, with the addition of practical examples. 

Babies’ SLegcntive’s (Gcowctep and tErlgoiTomctrp—From the works of A. M. 
Legendre, with the addition of a Treatise on Mensuration of Planes and 
Solids, and a Table of Logarithms and Logarithmic Sines. 

Babies’ JSttrbeplng—With a description and plates of the Theodolite, Com¬ 
pass, Plane-Table, and Level ; also, Maps of the Topographical Signs adopted 
by the Engineer Department—an explanation of the method of surveying the 
Public Lands, Geodesic and Maritime Surveying, and an Elementary Treatise 
on Navigation. 

Babies’ BcscrLpttbc (Geomctri)—With its application to Spherical Projec¬ 
tions. 

Babies’ Sbabes, Spabobis, and SLlitear ijperspeettbe. 

Babies’ Stnalptlcal CKeometrp—Embracing the Equations of the Point and 
Straight Line —of the Conic Sections —of the Line and Plane in Space ; 
also, the discussion of the General Equation of the second degree, and of Sur¬ 
faces of the second order. 

Babies’ Btfferenttal and Xutcgval (Calculus. 

Babies’ ILoglc anb Sdtllltp of ifttatljematlcs. 


Entered according to Act of Congress, in the year one thousand eight hundred and 
fifty-one, by Charles Davies, in the Clerk’s Office of the District Court of the 
United States for the Southern District ot^c^ York. 


J. P. JONES & CO., SXEREOTYPEKS. 




< l 


Benjamin Tuake c 
April 25, lWl 





rb^i 


PREFACE. 


The Elements of Surveying, first published in 1830, 
was designed as a text-book for the pupils of the Military 
Academy, and in its preparation little regard was bad to 
the supposed wants of other institutions. 

The work, however, was received by the public with 
more favor than was anticipated, and soon became a lead¬ 
ing text-book in the Colleges, the Academies, and the 
higher grade of Schools. 

For the purpose of adapting it, more fully, to the sup¬ 
posed wants of these institutions many changes have been 
made, since its first publication, and the present edition 
will be found to differ, in many respects, from those which 
have preceded. 

It has been the intention to begin with the very ele¬ 
ments of the subject, and to combine those elements in 
the simplest manner, so as to render the higher branches 
of plane surveying comparatively easy. All the instru¬ 
ments needed for plotting have been carefully described; 
and the uses of those required for the measurement of 
angles are fully explained. 

* 

The conventional signs adopted by the Topographical 
Bureau, which are now used by the United States Engi¬ 
neers in all their Charts and Maps, are given in plates 
5 and 6. 

Should these signs be generally adopted in the country, 
it would give entire uniformity to all maps and delinea¬ 
tions of the ground, and would establish a kind of lan¬ 
guage by which all the peculiarities of soil and surface 
could be accurately represented. 


271# 



ly 


PREFACE. 


A section has also been added on Geodesy. This 
branch of Surveying is extensively applied in the Coast 
Survey, and now forms an important element of a practi¬ 
cal or scientific education. 

A full account is also given of the manner of survey¬ 
ing the public lands; and, although the method is simple, 
it has, nevertheless, been productive of great results, by 
defining, with mathematical precision, the boundaries of 
lands in the new States, and thus settling their titles on 
an indisputable basis. 

This method was originated by Col. Jared Mansfield, 
whose great acquirements in science introduced him to the 
notice of President Jefferson, by whom he was appointed 
surveyor-general of the North-Western Territory. 

May it be permitted to one of his pupils, and a gradu¬ 
ate of the Military Academy, further to add, that at the 
organization of the institution in 1812, he was appointed 
Professor of Natural and Experimental Philosophy. This 
situation he filled for sixteen years, when he withdrew 
from the Academy to spend the evening of his life in re¬ 
tirement and study. His pupils, who had listened to his 
instructions with delight, who honored his learning and 
wisdom, and had been brought near to him by his kind 
and simple manners, have placed his portrait in the public 
library, that the institution might possess an enduring 
memorial of one of its brightest ornaments and distin¬ 
guished benefactors. 

At the solicitation of several distinguished teachers, there 
is added, in the present edition, an article on Plane Sail¬ 
ing, most of which has been taken, by permission of the 
author, from an excellent work on Trigonometry’and its 
applications, by Professor Charles W. Hackley. 

Fishkill Landing, 

July, 1851. 


CONTENTS. 


BOOK I. 

SECTION I. 

PAGE. 

Of Logarithms,. 9 

Table of Logarithms,. 11 

Multiplication by Logarithms,. 15 

Division by Logarithms,. 16 

Arithmetical Complement,. 17 

SECTION II. 

Geometrical Definitions,. 19 

Geometrical Constructions,. 25 

Description of Instruments,. 25 

Dividers,. 25 

Ruler and Triangle,. 25 

Scale of Equal Parts,. 27 

Diagonal Scale of Equal Parts,. 27 

Scale of Chords,. 29 

Semicircular Protractor,_ 30 

Sectoral Scale of Equal Parts,_ 30 

Gunter’s Scale,. 32 

Solution of Problems,. 32 

SECTION III. 

Plane Trigonometry,. 38 

Division of the Circumference,. 38 

Definitions of the Trigonometrical Lines,. 39 

Table of Natural Sines,. 40 

Table of Logarithmic Sines,. 41 

Theorems,. 44 

Solution of Triangles,. 48 

Solution of Right-Angled Triangles,. 54 

Application to Heights and Distances,. 55 





























VI 


CONTENTS. 


BOOK II. 

PLANE SURVEYING. 

SECTION I. 

PAGE. 

Definitions,. 64 

Measurement of Lines and Angles,. 66 ' 

Measures for Distances,. 66 

To Measure a Horizontal Line,. 67 

Measurement of Angles,. 69 

Of the Theodolite,. 69 

Verniers,. 75 

To Measure a Horizontal Angle with the Theodolite,.. 77 

To Measure a Vertical Angle,. 78 

Measurements with the Tape or Chain,. 79 

Surveying Cross,... 81 

SECTION II. 

Area, or Contents of Ground,., 85 

Of Laying out Land,. 96 

SECTION III. 

The Circumferenter, or Surveyor’s Compass,. 98 

Surveying with the Compass, Definitions, etc.,. 99 

Field Operations,. 102 

Traverse Table,. 105 

Of Balancing the Work,. 109 

Of the Double Meridian Distances of the Courses,. 112 

Of Finding the Area,.*. 114 

First Method of Plotting,. 117 

Second Method of Plotting,. 117 

Problems,. 118 

Offsets,. 122 

Of Supplying Omissions in the Field Notes,. 124 

To Determine the Angle between two Courses,. 126 

Of Dividing Land,... 127 

/ 

SECTION IV. 

Method of Surveying the Public Lands,. 131 

Variation of the Needle,. 134 

Method of Ascertaining the Variations,. 138 

To Find the True Meridian with the Theodolite,. 140 

To Find the True Meridian with the Compass,. 141 


































CONTENTS. 


y 11 


# 


BOOK III. 

LEVELLING AND TOPOGRAPHICAL SURVEYING. 

SECTION I. 

PAGE. 

Of Levelling,. 145 

The Y Level,.. 147 

The Water Level,. 150 

Levelling Staves,. 151 

Levelling in the Field,. 153 

Difference of Level between Two Points,. 153 

Example,. 154 

Levelling for Section,. 157 

Plotting the Section or Profile,. 158 

SECTION 11. 

Topographical Surveying,. 159 

Field Notes,..._. 166 

Pitting the Work,. 167 

BOOK IY. 

GEODESIC, TRIGONOMETRIC, AND MARITIME 

SURVEYING. 

SECTION I. 

Geodesic and Trigonometric Surveying,... 172 

Preliminary Reconnoissance and Establishment of Signals,. 174 

Measurement of a Base Line,. 176 

Triangulation,. 178 

Filling up the Survey,. 181 

Use of the Compass,.'_ 181 

The Plane Table—Its Uses,. 183 

To Measure a Horizontal Angle,. 185 

To Determine Lines in Extent and Position,. 185 

Of Changing the Paper,. 187 

Reduction to the Centre,. 189 

Spherical Excess,. 190 

Plotting the Triangulation,. 192 

The Circular Protractor,. 192 

To Lay off an Angle with the Protractor,. 193 

First Method of Plotting,... 193 

Second Method of Plotting,..... 194 

Method of Chords,. 195 

To Lay off an Angle,. 196 

SECTION 11. 

Maritime Surveying,. 197 


































VI11 


CONTENTS. 


BOOK Y. 

OF NAVIGATION. 

SECTION I. 

PAGE. 

Definitions,.201 

SECTION II. 

Of Plane Sailing,. 205 

SECTION III. 

Of Traverse Sailing,. 207 

Of Plotting,. 209 

SECTION IV. 

Parallel Sailing,...- 211 

section v. 

Middle Latitude Sailing,. 214 

Mercator’s Sailing,.„...218 

Mercator’s Chart,.221 

Line of Meridional Parts on Gunter’s Scale,. 222 











ELEMENTS OE SURVEYING. 


BOOK I. 

SECTION I. 

OF LOGARITHMS. 

1. The logarithm of a number is the exponent of the power 
to which it is necessary to raise a fixed number , in order to 
produce the first number. 

This fixed number is called the base of the system, and 
may be any number except 1: in the common system, 10 
is assumed as the base. 

2. If we form those powers of 10, which are denoted 
by entire exponents, we shall have 

10 °= 1 10 ' = 10 , 10 3 = 1000 

10 s = 100, 10 4 = 10000, &c., &c., 

From the above table, it is plain, that 0, 1, 2, 3, 4, &c., 
are respectively the logarithms of 1, 10, 100, 1000, 10000, 
&c.; we also see, that the logarithm of any number be¬ 
tween 1 and 10, is greater than 0 and less than 1: thus, 

log 2 = 0.301030. 

The logarithm of any number greater than 10, and less 
than 100, is greater than 1 and less than 2: thus, 

log 50 = 1.698970. 

The logarithm of any number greater than 100, and 
less than 1000, is greater than 2 and less than 3: thus, 

log 126 = 2.100371, &c. 



10 


ELEMENTS OF SURVEYING 


[BOOK I. 


If the above principles be extended to other numbers, 
it will appear, that the logarithm of any number, not an 
exact power of ten, is made up of two parts, an entire and 
a decimal part. The entire part is called the characteristic 
of the logarithm , and is always one less than the number of 
places of figures in the given number. 

8. The principal use of logarithms, is to abridge nu¬ 
merical computations. 

Let M denote any number, and let its logarithm be 
denoted by m; also let N denote a second number whose 
logarithm is n; then, from the definition, we shall have, 

10 m - M (1) 10 n = JST (2). 

Multiplying equations (1) and (2), member by member, 
we have* 

10 m + n = Mx N or, m + n= log (. M X N) ; hence, 

The sum of the logarithms of any two numbers is equal to 
the logarithm of their product 

4. Dividing equation (1) by equation (2), member by 
member, we have, 

m _„ M M 

10 = ^7 or, m — n — log hence, 

The logarithm of the quotient of tivo numbers, is equal to 
the logarithm of the dividend diminished by the logarithm of 
the divisor. 

0 

5. Since the logarithm of 10 is 1, the logarithm of the 
product of any number by 10, will be greater by 1 than the 
logarithm of that number ; also, the logarithm of the quotient 
of any number divided by 10, will be less by 1 than the 
logarithm of that number. 

Similarly, it may be shown that if any number be mul- 
iplied by one hundred, the logarithm of the product will 
be greater by 2 than the logarithm of that number; and 
if any number be divided by one hundred, the logarithm 
of the quotient will be less by 2 than the logarithm of 
that number, and so on. 


SEC. L] 

LOGARITHMS. 11 



EXAMPLES. 



log 827 

is 

2.514548 


log 32.7 

u 

1.514548 


log 3.27 

It 

0.514548 

0 

log .327 

it 

' 1.514548 


log .0327 

It 

2.514548 

From 

the above examples, we 

see, that in a number 


composed of an entire and decimal part, we may change 
tlie place of the decimal point without changing the deci 
mal part of the logarithm; but the characteristic is dimin¬ 
ished by 1 for every place that the decimal point is removed to 
the left. 

In the logarithm of a- decimal, the characteristic becomes 
negative, and is numerically 1 greater than the number of 
ciphers immediately after the decimal point. The negative 
sign extends only to the characteristic, and is written over 
it, as in the examples given above. 

TABLE OF LOGARITHMS. 

6 . A table of logarithms, is a table in which are writ¬ 
ten the logarithms of all numbers between 1 and some 
given number. The logarithms of all numbers between 1 
and 10,000 are given in the annexed table. Since rules 
have been given for determining the characteristics of 
logarithms by simple inspection, it has not been deemed 
necessary to write them in the table, the decimal part 
only being given. The characteristic, however, is given 
for all numbers less than 100. 

The left hand column of each page of the table, is the 
column of numbers, and is designated by the letter IT; 
the logarithms of these numbers are placed opposite them 
on the same horizontal line. The last column on each 
page,. headed D, shows the difference between the loga¬ 
rithms of two consecutive numbers. This difference is 
found by subtracting the logarithm under the column 
headed 4, from the one in the column headed 5 in the 
same horizontal line, and is nearly a mean of the differ¬ 
ences of any two consecutive logarithms on this line. 


12 


ELEMENTS OF SURVEYING. 


[BOOK I 


To find , from the table , the logarithm of any number. 

* 

7. If the number is less than 100, look on the first page 
of the table, in the column of numbers under 1ST, until the 
number is found: the number opposite is the logarithm 

ought: Thus, 

log 9 = 0.954243. 

• 

When the number is greater than 100 and less than 10000. 

8 . Find in the column of numbers, the first three figures 
of the given number. Then pass across the page along a 
horizontal line until you come into the column under the 
fourth figure of the .given number: at this place, there are 
four figures of the required logarithm, to which two figures 
taken from the column marked 0, are to be prefixed. 

If the four figures already found stand opposite a row 
of six figures in the column marked 0, the two left hand 
figures of the six, are the two to be prefixed; but if they 
stand opposite a row of only four figures, you ascend the 
column till you find a row of six figures; the two left 
hand figures of this row are the two to be prefixed. If 
you prefix to the decimal part thus found, the character¬ 
istic, you will have the logarithm sought: Thus, 

log 8979 = 3.953228 
log .08979 = 2.953228 

If, however, in passing back from the four figures found, 
to the 0 column, any dots be met with, the two figures 
to be prefixed must be taken from the horizontal line di¬ 
rectly below: Thus, 

log 3098 = 3.491081 
log 30.98 = 1.491081 

If the logarithm falls at a place where the dots Occur 
0 must be written for each dot, and the two figures to be 
prefixed are, as before, taken from the line below: Thus, 

log 2188 = 3.340047 
log .2188 = 1.340047 


I 


SEC. L] LOGARITHMS. 13 

When the number exceeds 10,000. 

9. Tlie characteristic is determined by the rules already 
given. To find the decimal part of the logarithm: place 
a decimal point after the fourth figure from the left 
hand, converting the given number into a whole number 
and decimal. Find the logarithm of the entire part by the 
rule just given, then take from the right hand column of 
the page, under D, the number on the same horizontal 
line with the logarithm, and multiply it by the decimal 
part; add the product thus obtained to the logarithm al¬ 
ready found, and the sum will be the logarithm sought. 

If, in multiplying the number taken from the column 
D, the decimal part of the product exceeds .5, let 1 be 
added to the entire part; if it is less than .5, the decimal 
part of the product is neglected. 

EXAMPLE. 

1. To find the logarithm of the number 672887. 

The characteristic is 5.; placing a decimal point after 
the fourth figure from the left, we have 6728.87. The 
decimal part of the log 6728 is .827886, and the corres¬ 
ponding number in the column D is 65; then 65X.87= 
56.55, and since the decimal part exceeds .5, we have 57 
to be added to .827886, which gives .827943. 

Hence, log 672887 = 5.827943 

Similarly, log .0672887 = 2.827943 

The last rule has been deduced under the supposition 
that the difference of the numbers is proportional to the 
difference of their logarithms, which is sufficiently exact 
within the narrow limits considered. 

In the above example, 65 is the difference between the 
logarithm of 672900 and the logarithm of 672800, that is, 
it is the difference between the logarithms of two numbers 
vhich differ by 100. 

We have then the proportion 

100 : 87 : : 65 : 56.55, 

hence, 56.55 is the number to be added to the logarithm 
before found. 


14 ELEMENTS OF SURVEYING. [BOOK I. 

To find from the table the number corresponding to a given 

10. Search, in the columns of logarithms for the decimal 
part of the given logarithm: if it cannot he found in the 
table 7 take out the number corresponding to the next less 
logarithm and set it aside. Subtract this less logarithm 
from the given logarithm, and annex to the remainder as 
many zeros as may be neces’sary, and divide this result by 
the corresponding number taken from the column marked 
D, continuing the division as long as desirable: annex the 
quotient to the number set aside. Point off, from the left 
hand, as many integer figures as there are units in the 
characteristic of the given logarithm increased by 1; the 
result is the required number. 

If the characteristic is negative, the number will be 
entirely decimal, and the number of zeros to be placed at 
the left of the number found from the table, will be equal to 
the number of units in the characteristic diminished by 1. 

This rule, like its converse, is founded on the supposi¬ 
tion that the difference of the logarithms is proportional 
to the difference of their numbers within narrow limi ts 

EXAMPLE. 

1. Find the number corresponding to the logarithm 
3^233568. 

The decimal part of the given logarithm is .233568 

The next less logarithm of the table is .233504, 

and its corresponding number 1712. - 

Their difference is - - 64 

Tabular difference 253)6400000(25 

Hence, the number sought 1712.25. . 

The number corresponding to the logarithm 3.233568 
is .00171225. 

2 . What is the number corresponding to the logarithm 

2.785407? Ans. .06101084. 

3. What is the number corresponding to the logarithm 

1.846741? * Ans. .702653. 




SEC. L] 


15 


LOGARITHMS. 

MULTIPLICATION BY LOGARITHMS. 

11. When it is required to multiply numbers by means 
of their logarithms, we first find'from the table the loga¬ 
rithms of the numbers to be multiplied; we next. add 
these logarithms together, and their sum is the logarithm 
of the product of the numbers (Art. 3). 

The term sum is to be understood in its algebraic 
sense; therefore, if any of the logarithms have negative 
characteristics, the difference between their sum and that 
of the positive characteristics, is to be taken; the sign of 
the remainder is that of the greater sum. 

* 

EXAMPLES. 

1 . Multiply 23.14 by 5.062. 

log 23.14*= 1.364363 
log 5.062 = 0.704322 

Product, 117.1347 . . . 2.068685 

2. Multiply 3.902, 597.16, and 0.0314728 together. 

log 3.902 = 0.591287 
log 597.16 = 2.776091 
log 0.0814728 = 2.497936 

Product, 73.3354 .... 1.865314 

Here, the 2 cancels the + 2, and the 1 carried from 
the decimal part is set down. 

3. Multiply 3.586, 2.1046, 0.8872, and 0.0294 together. 

log 3.586 = 0.554610 
log 2.1046 = 0.823170 . 
log 0.8372 = 1.922829 
log 0.0294 = 2.468347 

Product, 0.1857615 . . 1.268956 

In this example the 2, carried from the decimal part, 
cancels 2, and there remains 1 to be set down. 








16 


ELEMENTS OF SURVEYING. 


[BOOK I. 


DIVISION OF NUMBERS BY LOGARITHMS. 

12. When it is required to divide numbers by means 
of their logarithms, we liave only to recollect, that the 
subtraction of logarithms corresponds to the division of 
their numbers (Art. 4). Hence, if we find the logarithm 
of the dividend, and from it subtract the logarithm of the 
divisor, the remainder will be the logarithm of the quotient. 

This additional caution may be added. The difference 
of the logarithms, as here used, means the algebraic differ¬ 
ence; so that, if the logarithm of the divisor have a nega¬ 
tive characteristic, its sign must be changed to positive, 
after diminishing it by the unit, if any, carried in the sub¬ 
traction from the decimal part of the logarithm. Or, if 
the characteristic of the logarithm of the dividend is nega¬ 
tive, it must be treated as a negative number. 

* 

EXAMPLES. 

1. To divide 24163 by 4567. 

log 24163 = 4.383151 
log 4567 = 3.659631 

Quotient, 5.29078 . . 0.723520 


2. To divide 0.06314 by .007241. 

log 0.06314 = 2.800305 
log 0.007241 = 3.859799 

Quotient, 8.7198 . . 0.940506 


Here, 1 carried from the decimal part to the 3, changes 
it to 2, which being taken from 2, leaves 0 for the cha¬ 
racteristic. 

3. To divide 37.149 by 523.76. 

log 37.149 = 1.569947 
log 523.76 = 2.719133 

Quotient, 0.0709274 . 2.850814 








SEC. I] 


LOGARITHMS. 


17 


4. To divide 0.7438 by 12.9476. 

log 0.7438 = 1.871456 
log 12.9476 = 1.112189 

Quotient, 0.057447 . . 2.759267 

Here, the 1 taken from f, gives 2 for a result, as set 
down. 


ARITHMETICAL COMPLEMENT. 

13. The Arithmetical complement of a logarithm is the 
number which remains after subtracting the logarithm 
from 10 . 

Thus, 10 - 9.274687 = 0.725313. 

Hence, 0.725313 is the arithmetical complement 

of 9.274687. 

■% 

14. We will now show that, the difference between two 
logarithms is truly found , by adding to the first logarithm the 
arithmetical complement of the logarithm to be subtracted , and 

then diminishing the sum by 10 . 

♦ 

Let a = the first logarithm, 

5 = the logarithm to be subtracted, 
and c= 10 — Z> = the arithmetical complement of b. 

How the difference between the two logarithms will be 
expressed by a — b. 

But, from the equation c = 10 — b, we have 

c — 10 — — bj 

hence, if we place for — b its value, we shall have 

a — b = a + c —10 , 

which agrees with the enunciation. 

When we wish the arithmetical complement of a loga¬ 
rithm, we may write it directly from the table, by subtract¬ 
ing the left hand figure from 9 , then proceeding to the right , 
subtract each figure from 9 till ice reach the last significant 
figure, which must be taken from 10 : this will be the same 
as taking the logarithm from 10 . 

2 


\ 




18 


ELEMENTS OF SURVEYING. 


[BOOK I 


EXAMPLES. 

1. From 8.274107 take 2.104729. 

By common method. By arith. comp. 

8.274107 3.274107 

2.104729 its ar. comp. 7.895271 

Diff. 1.169378 Sum 1.169378 after sub¬ 

tracting 10 . 

Hence, to perform division by means of tlie arithmetical 
complement, we have the following 

RULE. 

To the logarithm of the dividend add the arithmetical com¬ 
plement of the logarithm of the divisor: the sum , after sub¬ 
tracting 10, will be the logarithm of the quotient. 

* 

EXAMPLES. 

1 . Divide 827.5 by 22.07. 

log 827.5 . 2.515211 

log 22.07 ar. comp. 8.656198 

Quotient, 14.839 . . . 1.171409 

2 . Divide 0.7438 by 12.9476. 

. log 0.7438 .... 1.871456 
log 12.9476 ar. comp. 8.887811 

Quotient, 0.057447 . . . 2.759267 

In this example, the sum of the characteristics is 8 , 
from which, taking 10 , the remainder is 2 . 

3. Divide 37.149 by 523.76. 

log 37.149 .... 1.569947 

log 523.76 ar. comp. 7.280867 

Quotient, 0.0709273 . . 2.850814 












SEC. II] GEOMETRICAL DEFINITIONS. 


19 


4. Divide 0.875 by 25. 

5. Divide 8.1416 by .944. 

6 . Divide 2756 by 827. 

7. Divide 672859 by 0.09657. 


Ans. 0.085. 
Ans. 8.8279. 
Ans. 8.4281. 
Ans. 6967580.64. 


SECTION II. 

GEOMETRICAL DEFINITIONS AND CONSTRUCTIONS. 

1. Extension bas three dimensions, length, breadth, 
and thickness. 

2. Geometry is the science which has for its object: 

1st. The measurement of extension; and 2dly. To dis¬ 
cover, by means of such measurement, the properties and 
relations of geometrical figures. 

8. A Point is that which has place, or position, but 
not magnitude. 

4. A Line is length, without breadth or thickness. 

5. A Straight Line is one which 
lies in the same direction between any 
two of its points. 

6. A Broken Line is one made up 
of straight lines, not lying in the same 
direction. 

7. A Curve Line is one which 
changes its direction at every point. 

The word line when used alone, will designate a straight 
line; and the word curve, a curve line. 

8. A Surface is that which has length and breadth 
without thickness. 






20 


ELEMENTS OF SURVEYING. 


[BOOK I. 


9. A TPlane is a surface, such, that if any two of its 
points he joined by a straight line, such line will be wholly 
in the surface. 

10. Every surface, which is not a plane surface, or com¬ 
posed of plane surfaces, is a curved surface. 

11. A Solid, or Body is that which has length, breadth, 
and thickness: it therefore combines the three dimensions 
of extension. 

12. An Angle is the portion of a plane included be¬ 
tween two straight lines which meet at a common jioint. 
The two straight lines are called the sides of the angle, 
and the common point of intersection, the vertex . 

Thus, the part of the plane includ- (y 

ed between AB and A G is called an 
angle: AB and A G are its sides, and A s' 

its vertex. 

An angle is sometimes designated aA— - 

simply by a letter placed at the vertex, 
as, the angle A ; but generally, by three letters, as, the 
angle BAG or GAB ,—the letter at the vertex being always 
placed in the middle. 

13. When a straight line meets an¬ 
other straight line, so as to make the 
adjacent angles equal to each other, 
each angle is called a right angle ; and 

the first line is said to be perpendicu - -- 

lar to the second. 


14. An Acute Angle is an angle 
less than a right angle. 



15. An Obtuse Angle is an angle 
greater than a right angle. 








S E C. 11.] 


GEOMETRICAL DEFINITIONS 


21 


16. Two straight lines are said to 

be parallel, when being situated in_ 

the same plane, they cannot meet, how 
far soever, either way, both of them 
be produced. 

17. A Plane Figure is a portion of a plane terminat¬ 
ed on all sides by lines, either straight or curved. 

18. A Polygon, or rectilineal fig¬ 
ure, is a portion of a plane terminat¬ 
ed on all sides by straight lines. 

The sum of the bounding lines is 
called the perimeter of the polygon. 

19. The polygon of three sides, the simplest of all, is 
called a triangle; that of four sides, a quadrilateral; that 
of five, a pentagon; that of six, a hexagon; that of seven, 
a heptagon; that of eight, an octagon; that of nine, an 
nonagon; that of ten, a decagon; and that of twelve, a 
dodecagon. 

20. An Equilateral polygon is one which has all its 
sides equal; an equiangular polygon, is one which has all 
its angles equal. 

21. Two polygons are mutually equilateral, when they 
have their sides equal each to each, and placed in the 
same order: that is to say, when following their bounding 
lines in the same direction, the first side of the one is 
equal to the first side of the other, the second to the 
second, the third to the third, and so on. 

22. Two polygons are mutually equiangular , when every 
angle of the one is equal to a corresponding angle of the 

other, each to each. 

23. Triangles are divided into classes with reference 
both to their sides and angles. 

1. An equilateral triangle is one 
which has its three sides equal. 








22 


ELEMENTS OF SURVEYING. [BOOK I. 


2. An isosceles triangle is one wliicli 
lias only two of its sides equal. 



/ 

3. A scalene triangle is one which has 
its three sides unequal. 



4. An acute-angled triangle is one 
which lias its three angles acute. 



5. A right-angled triangle is one which 
has a right angle. The side opposite the 
right angle is called the hypothenuse , and 
the other two sides, the base and perpen¬ 
dicular. 


6. An obtuse-angled triangle is one 
which has an obtuse angle. 




24. There are three kinds of Quadrilaterals: 


1. The trapezium , which has none of 
its sides parallel. 



2. The trapezoid , which has only two 
of its sides parallel. 



3. The parallelogram , which has its 
opposite sides parallel. 













SEC. II] GEOMETRICAL DEFINITIONS. 


23 


25. There are four kinds of Parallelograms: 

1. The rhomboid , which has no right 
angle. 

♦ 



2. The rhombus , or lozenge , which is 
an equilateral rhomboid. 


3. The rectangle , which is an equian¬ 
gular parallelogram, but not equilateral. 


4. The square , which is both equilat¬ 
eral and equiangular. 


A Diagonal of a figure is a line 
which joins the vertices of two angles 
not adjacent. 



EXPLANATION of signs. 

26. The sign = is the sign of equality; thus, the ex¬ 
pression A — B : signifies that A is equal to B. 

27. To signify that A is smaller than A, the expression 
A < B is used. 

28. To signify that A is greater than B , the expression 
Ay B is used; the smaller quantity being always at the 
vertex of the angle. 

29. The sign. + is called plus; it indicates addition. 









24 . ELEMENTS OF SURVEYING. [BOOK I. 

30. The sign — is called minus; it indicates subtraction: 
Thus, A -f B, represents the sum of the quantities A 

and B; A — B represents their difference, or what remains 
after B is taken from A ; and A — B + C ) or A + G — B, 
signifies that A and 0 are to be added together, and that 
B is to be subtracted from their sum. 

31. The sign X indicates multiplication : thus A X B 
represents the product of A and B. 

The expression A X ( BA C — D) represents the product 
of A by the quantity BA C — D. If A AD were to be 
multiplied by A —BA C, the product would be indicated 
thus; 

{A + D') X ( A — B -f- C\ 

whatever is enclosed within the curved lines, being consid¬ 
ered as a single quantity. The same thing may also be 
indicated by a bar: thus, 

A ABA Gx D, 

denotes that the sum of A, B and C, is to be multiplied 

by D. 

32. A figure placed before a line, or quantity, serves 
as a multiplier to that line or quantity; thus, 3 AB signi¬ 
fies that the line AB is taken three times; \A signifies the 
half of the angle A. 


33. The square of the line AB is designated by AB ~; 

its cube by AB . What is meant by the square and cube 
of a line is fully explained in Geometry. 


34. The sign ^ indicates a root to be extracted; thus, 

■y/2 means the square-root of 2 ; y/ A X B means the square- 
root of the product of A and B. 






SEC. II] GEOMETRICAL CONSTRUCTIONS. 


25 


GEOMETRICAL CONSTRUCTIONS. 

35. Before explaining the method of constructing geo¬ 
metrical problems ; we shall describe some of the simpler 
instruments and their uses. 


DIVIDERS. 



36. The dividers is the most simple and useful of the 
instruments used for drawing. It consists of two legs ba , 
be, which may be easily turned around a joint at b. 

One of the principal uses of this instrument is to lay 
off on a line, a distance equal to a given line. 

For example, to lay oh on CD a distance equal to AB. 

For this purpose, place the forefin¬ 
ger on the joint of the dividers, and A\ - \B 

set one foot at A: then extend, with 

the thumb and other fingers, the Cl E D 

other leg of the dividers, until its foot reaches the point 
B. Then raise the dividers, place one foot at C, and 
mark with the other the distance CD: this will evidently 
be equal to AB. 


RULER AND TRIANGLE. 




37. A Euler of convenient size, is about twenty inches 
in length, two inches wide, and a fifth of an inch in thick- 












26 


ELEMENTS OF SURVEYING. [BOOK I. 

ness. It should, be made of a hard material, perfectly 
straight and smooth. 

The hypothenuse of the right-angled triangle, which is 
used in connection with it, should be about ten inches in 
length, and it is most convenient to have one of the sides 
considerably longer than the other. We can solve, with 
the ruler and triangle, the two following problems. 


I. To draw through a given point a line which shall be paral¬ 
lel to a given line. 


38. Let 0 be the given point, and AB the given line. 

Place the hypothenuse of the tri- c 

angle against the edge of the ruler, 
and then place the ruler and triangle 
on the paper, so that one of the 
sides of the triangle shall coincide exactly with AB: the 
triangle being below the line. 


A 


B 


Then placing the thumb and fingers of the left hand 
firmly on the ruler, slide the triangle with the other hand 
along the ruler until the side which coincided with AB 
reaches the point C. Leaving the thumb of the left hand 
on the ruler, extend the fingers upon the triangle and hold 
it firmly, and with the right hand, mark with a pen or 
pencil, a line through C: this line will be parallel to AB. 


II. To draiv through a given point a line which shall be per¬ 
pendicular to a given line. 

39. Let AB be the given line, and D the given point. 

Place the hypothenuse of the tri¬ 
angle against the edge of the ruler, as 

before. Then place the ruler and ______ 

triangle so that one of the sides of A I} B 
the triangle shall coincide exactly with the line AB. 
Then slide the triangle along the -ruler until the other 
side reaches the point I): draw through D a right line, 
and it will be perpendicular to AB. 






SEC. II.] GEOMETRICAL CONSTRUCTIONS. 


27 


SCALE OF EQUAL PARTS. 


a 



| .1 .8 -ft. A .5 .6 .7 .8 .D7Q 

~! I i : i. i -1—J—J ..J. 

a I b 


40. A scale of equal parts is formed by dividing a line 
of a given length into equal portions. 

If, for example, the line ah of a given length, say one 
inch, be divided into any number of equal parts, as 10, 
the scale thus formed, is called a scale of ten parts to the 
inch. The line ah, which is divided, is called the unit of 
the scale. This unit is laid off several times on the left 
of the divided line, and the points marked 1, 2, 3, &c. 

The unit of scales of equal parts, is, in general, either 
an inch, or an exact part of an inch. If, for example, ah, 
the unit of the scale, were half an inch, the scale would 
be one of 10 parts to half an inch, or of 20 parts to the 
inch. 

If it were required to take from the scale a line equal 
to two inches and six-tenths, place one foot of the dividers 
at 2 on the left, and extend the other to .6, which marks 
the sixth of the small divisions: the dividers will then 
embrace the required distance. 


DIAGONAL SCALE OF EQUAL PARTS. 






1 1 1 1 1 1 1 II 


-oy 


I I i I I I I I 


•08 


1 1 1 191 1 1 1 


..07 

1 1 1 1 1 

i i 


.06 

1 

III 

i i i 


-05 


1 \c 

III 1 


.04 


1 1 


rrrr 


.03 


1 1 


i 1 1 


•02 

iiii 


i i i 


.01 

LLLLi 


iiii 


2 1 a .1 .2 .3.4 ,5 .6.7.8.9 b 

h £/ 


41. This scale is thus constructed. Take ab for the 
unit of the scale, which may be one inch, -J, J- or f of an 
inch, in length. On ah describe the square abed. Divide 
the sides ah and clc each into ten equal parts. Draw af 
and the other nine parallels as in the figure. 

Produce ha to the left, and lay off the unit of the 
scale any convenient number of times, and mark the points 































28 


ELEMENTS OF SURVEYING. 


[BOOK I. 


1, 2, 8, &c. Then, divide the line ad into ten equal parts, 
and through the points of division draw parallels to ab, as 
in the figure. 

Now, the small divisions of the line ab are each one- 
tenth (.1) of ab; they are therefore .1 of ad, or .1 of ag 
or gh. 

' If we consider the triangle adf, we see that the base df 
is one-tenth of ad, the unit of the scale. Since the distance 
from a to the first horizontal line above ab, is one-tenth of 
the distance ad, it follows that the distance measured on that 
line between ad and af is one-tenth of df: but since one-tenth 
of a tenth is a hundredth, it follows that this distance is 
one hundredth (.01) of the unit of the scale. A like dis¬ 
tance measured on the second line will be two hundredths 
(.02) of the unit of the scale; on the third, .03 ; on the 
fourth, .04, &c. 

If it were required to take, in the dividers, the unit of 
the scale, and any number of tenths, place one foot of the 
dividers at 1, and extend the other to that figure between 
a and b which designates the tenths. If two or more 
units are required, the dividers must be placed on a point 
of division further to the left. 

When units, tenths, and hundredths, are required, place 
one foot of the dividers where the vertical line through 
the point which designates the units, intersects the line 
which designates the hundredths: then, extend the dividers 
to that line between ad and be which designates the tenths: 
the distance so determined will be the one required. 

For example, to take off the distance 2.84, we place 
one foot of the dividers at l, and extend the other to e: 
and to take off the distance 2.58, we place one foot of the 
dividers at p and extend the other to q. 

Remark I. If a line is so long that the whole of it 
cannot be taken from the scale, it must be divided, and 
the parts of it taken from the scale in succession. 

Remark II. If a line be given upon the paper, its 
length can be found by taking it in the dividers and ap¬ 
plying it to the scale. 


SEC. II.] GEOMETRICAL CONSTRUCTION’S. 


29 


SCALE OF CHORDS. 



42. If, with, any radius, as A C, we describe the quad¬ 
rant CD, and then divide it into 90 equal parts, each part 
is called a degree. 

Through G\ and each point of division, let a chord be 
drawn, and let the lengths of these chords be accurately 
laid off on a scale: such a scale is called a scale of chords. 
In the figure, the chords are drawn for every ten de¬ 
grees. 

The scale of chords being once constructed, the radius 
of the circle from which the chords were obtained, is 
known; for, the chord marked 60 is always equal to the 
radius of the circle. A scale of chords is generally laid 
down on the scales which belong to cases of mathematical 
instruments, and is marked cho. 

To lay off, at a given point of a line, with the scale of chords , 

an angle equal to a given angle. 

43. Let AB be the line, and A the given point. 

Take from the scale the chord of 60 

degrees, and with this radius and the 
point A as a centre, describe the arc 
BC. Then take from the scale the 
chord of the given angle, say 30 de¬ 
grees, and with this line as a radius, and A as a centre, 
describe an arc cutting BC in C. Through A and C 
draw the line AC y and BAG will be the required angle. 








30 


ELEMENTS OF SURVEYING. 


[BOOK I. 


SEMICIRCULAR PROTRACTOR. 
C 



44. This instrument is used to lay down, or protract 
angles. It may also be used to measure angles included 
between lines already drawn upon paper. 

It consists of a brass semicircle, ABO, divided to half . 
degrees. The degrees are numbered from 0 to 180, both 
ways; that is, from A to B and from B to A. The di¬ 
visions, in the figure, are made only to degrees. There 
is a small notch at the middle of the diameter AB, which 
indicates the centre of the protractor. 

To lay off an angle with a Protractor. 

45. Place the diameter AB on the line, so that the 
centre shall fall on the angular point. Then count the 
degrees contained in the given angle from A towards B , or 
from B towards A, and mark the extremity of the arc with 
a pin. Remove the protractor, and draw a line through 
the point so marked and the angular point: this line will 
make with the given line the required angle. 


SECTORAL SCALE OF EQUAL PARTS. 



















SEC. II.] GEOMETRICAL CONSTRUCTIONS. 


81 


46. The sector is an instrument generally made of ivory 
or brass. It consists of two arms, or sides, which open 
by turning round a joint at their common extremity. 

There are several scales laid down on the sector: those, 
however, which are chiefly used in drawing lines and 
angles, are, the scale of chords already described, and the 
scale of equal parts now to be explained. 

On each arm of the sector, there is a diagonal line 
that passes through the point about which the arms turn: 
these diagonal lines are divided into equal parts. 

On the sectors which belong to the cases of English 
instruments, the diagonal lines are designated by the letter 
Z, and numbered from the centre of the sector, 1, 2, 8, 4, 
5, 6, 7, 8, 9, 10, to the two extremities. On the sectors 
which belong to cases of French instruments, they are de¬ 
signated, u Les parties egales,” and numbered 10, 20, 30, 
40, &c., to 200. On the English sectors there, are 20 equal 
divisions between any two of the lines numbered 1, 2, 3, 
&c., so that there are 200 equal parts on the scale. 

The advantage of the sectoral scale of equal parts, is 
this— 

When it is proposed to draw a line upon paper, on 
such a scale that any number of parts of the line, 40 for 
example, shall be represented by one inch on the paper, or 
by any part of an inch, take the inch, or part of the inch, 
from the scale of inches on the sector: then, placing one 
foot of the dividers at 40 on one arm of the sector, open 
the sector until the other foot reaches to the corresponding 
number on the other arm: then lay the sector on the table 
without varying the angle. 

How, if we regard the lines on the sector as the sides 
of a triangle, of which the line 40, measured across, is the 
base, it is plain, that if any other line be likewise meas 
ured across the angle of the sector, the bases of the tri 
angles, so formed, will be proportional to their sides. 
Therefore, if we extend the dividers from 50 to 50, this 
distance will represent a line of 50, to the given-scale: 
and similarly for other lines. 


32 ELEMENTS OF SURVEYING. [BOOK I. 

I 

Let it now be required to lay down a line of sixty- 
seven feet, to a scale of twenty feet to the inch. 

Take one inch from the scale of inches: then place 
one foot of the dividers at the twentieth division, and 
open the sector until the dividers will just reach the twen¬ 
tieth division on the other arm: the sector is then set to 
the proper angle; after which the required distance to be 
laid down on the paper is found by extending the divi¬ 
ders from the sixty-seventh division on one arm, to the 
sixty-seventh division on the other. 

gunter’s scale. 

47. This is a scale of two feet in length, on the faces 
of which a variety of scales is marked. The face on 
which the divisions of inches are made, contains, however, 
all the scales necessary for laying down lines and angles. 
These are, the scale of equal parts, the diagonal scale of 
equal parts, and the scale of chords, all of which have 
been described. 


SOLUTION OF PROBLEMS REQUIRING THE USE OF THE IN¬ 
STRUMENTS THAT HAVE BEEN DESCRIBED. 

I 

I, At a given point in a given straight line , to ei'ect a perpen¬ 
dicular to the line. 


48. Let A be the given point, and BG the given line. 




From A lay off any two distances, 

AB and A G,\ equal to each other. 

Then, from the points B and C, as 
centres, with a radius greater than BA , 
describe two arcs intersecting each A lf~~ 

other in D: draw AD, and it will be the perpendicular 
required. 


II. From a given point without a straight line , to let fall a 

perpendicular on the line. 

49. Let A be the given point, and BD the given line. 




SEC. II] GEOMETRICAL CONSTRUCTION'S. 


33 




-D 


From the point i as a centre, A 

with a radius sufficiently great, 
describe an arc cutting the line 
BD in the two points B and D: 
then mark a point E\ equally dis- \(/ 

tant from tlie points B and D, E 

and draw AE: AE will be the perpendicular required. 


III. At a point , in a given line , to make an angle equal to a 

given angle. 

50. Let A be the given point, AE the given line, and 
IKL the given angle. 

From the vertex K, as a 
centre, with any radius, describe 
the arc IL, terminating in the 
two sides of the angle. From 
the point 1 as a centre, with a distance AE equal to KI, 
describe the arc ED; then take the chord LI, with which, 
from the point E as a centre, describe an arc cutting the 
indefinite arc DE\ in D; draw AD, and the angle EAD 
will be equal to the given angle K. 



IY. To divide a given angle , or a given arc f into two equal 

parts. 

51. Let C be the given angle, and AEB the arc which 
measures it. 

From the points A and B as 
centres, describe with the same 
radius two arcs cutting each other 
in D: through D and the centre 
0 draw CD: the angle ACE will 
be equal to the angle ECB, and 
the arc AE to the arc EB. 


a 



Y. Through a given point to draw a parallel to a given line. 

« 

52. Let A be the given point, and BC the given line. 









34 


[BOOK I 


ELEMENTS OF SURVEYING. 

From i as a centre, with a 
radius greater than the shortest 
distance from A to BC, describe 
the indefinite arc ED: from the 
point E as a centre, with the same radius, describe the 
arc AF; make EIJ — AF\ and draw AD: then will AD 
be the parallel required. 



YI. Two angles of a triangle being given , to find the third. 


53. Draw the indefinite line 
DEF. At the point A, make 
the angle DEG equal to one of 
the given angles, and the angle 
CETI equal to the other: the re¬ 
maining angle IIEF will be the 
third angle required. 



YII. To represent , on paper , a line of a given length , so that 

any number of its parts shall correspond to the unit of the 

scale. 

54. Suppose that the given line were 75 feet in length, 
and it were required to draw it on paper, on a scale of 25 
feet to the inch. 

The length of the line 75 feet, being divided by 25, 
will give 3, the number of inches which will represent the 
line on paper. 

Therefore, draw the indefinite line AB, on which lay 

i- 4 -*-1— B 

A C 

off a distance A 0 equal to 3 inches: A C will represent 
the given line of 75 feet, drawn on the required scale. 

Remark I. This problem explains the manner of repre- * 
enting a line upon paper, so that a given number of its 
parts shall correspond to the unit of the scale, whether 
that unit be an inch or any part of an inch. 

When the length of the line to be laid down is given, 
and it has been determined how many parts of it are to 







SEC. II.] GEOMETRICAL CONSTRUCTIONS. 


35 


be represented on tbe paper by a distance equal to the 
unit of the scale, we find the length which is to be taken 
from the scale by the following 


RULE. 

Divide the length of the line by the number of parts which 
is to be represented by the unit of the scale: the quotient will 
show the number of units which is to be taken from the scale. 


EXAMPLES. 


1. If a line of 640 feet is to be laid down on paper, on 
a scale of 40 feet to the inch; what length must be taken 
from the scale ? 


40)640(16 inches. 


2. If a line of 357 feet is to be laid down on a scale 
of 68 feet to the unit of the scale, (which we will suppose 
half an inch), how many parts are to be taken ? 


Ans. 


(5.25 parts, or 
( 2.625 inches. 


3. A line of 384 feet is drawn on paper, on a scale of 
45 feet to the inch; what is its length on the paper ? 

Ans. 8.53 inches. 


Bemark II. When the length of a line on the paper is 
given, and it is required to* find the true length of the 
line which it represents, take the line in the dividers and 
apply it to the scale, and note the number of units, and 
parts of a unit to which it is equal. Then multiply this 
number by the number of parts which the unit of the 
scale represents, and the product will be the length of the 
line. 

For example, suppose the length of a line drawn on 
the paper was found to be 3.55 inches, the scale being 40 
feet to the inch: then, 


3.55 X 40 = 142 feet, the length of the line. 


86 


EI/EMENTS OF SURVEYING. 


'[BOOK I. 


VIII. Having giveh two sides and the included angle of a tri- 

angle , to describe the triangle. 


55. Let the line B— 150 feet, and G = 120 feet, be the 
given sides; and A — 80 degrees, the given angle: to de¬ 
scribe the triangle on a scale of 200 feet to the inch. 


Draw the indefinite line DG ) and B 
at the point D ) make the angle GDH 
equal to 80 degrees: then lay off 
DG equal to 150, equal to three 
quarters of an inch, and DH equal 
to 120, equal to six tenths of an 
inch, and draw GII: DHG will be the required triangle. 



IX. The three sides of a triangle being given, to describe the 

triangle. 

56. Let A, B and (7, be the sides. 

Draw DE equal to the side A. 

From the point Das a centre, with 
a radius equal to the second side B , 
describe an arc: from E as a cen¬ 
tre, with a radius equal to the third 
side (7, describe another arc inter¬ 
secting the former in F; draw DF and EF,\ and DFE will 
be the triangle required. 







X. Having given two sides of a triangle and an angle oppo¬ 
site one of them , to describe the triangle. 

57. Let A and B be the given sides, and 0 the given 
angle, which we will suppose is opposite the side B. 

Draw the indefinite line DF 
and make the angle FDIT equal to 
the angle 0: take DH=A , from 
the point JTj as a centre, with a 
radius equal to the other given 
side, B ) describe an arc cutting 
DF in F; draw HE: then will DHF be the required tri¬ 
angle. 
















37 


SEC. II.] GEOMETRICAL CONSTRUCTIONS; 


/l'- 

Bt 



E 


If the angle C is acute, and 
the side B less than A, then 
the arc described from the 
centre E with the radius EF 
— B will cut the side BE in 
two points, F and G, lying on 
the same side of D: hence, there will be two triangles, 
DEF, and DEG , either of which will satisfy all the condi¬ 
tions of the problem. 



XI. The adjacent sides of a 'parallelogram , with the angle 
which they contain, being given , to describe the paral¬ 
lelogram. 

4 

58. Let A and B be the given sides, and C the given 
angle. 

Draw the line DH , and 
lay off DE equal to A; at 
the point D , make the angle 
EDF= G ; take DF=B: de¬ 
scribe two arcs, the one from 
F.\ as a centre, with a radius FG — DE, the other from E , as 
a centre, with a radius EG = DF; through the point G, 
where these arcs intersect each other, draw FG , EG ; DEGF 
will be the parallelogram required. 


D 

A 

B 


FL 

-q 


IE 


-1 / 


XII. To find the centre of a given circle or arc. 

59. Take three points, A , B , 0,\ any where in the cir¬ 
cumference, or in the arc: 
draw AB , BC; bisect these two 
lines by the perpendiculars, DE, 

FG: the point 0, where these 
perpendiculars meet, will be the 
centre sought. 

The same construction serves 
for making a circumference pass 
through three given points A, B\ 

C\ and also for describing a circumference, about a given 
triangle. 
















88 


ELEMENTS OF SURVEYING. 


[BOOK L 


PLANE TRIGONOMETRY. 


SECTION III. 

DEFINITIONS.—APPLICATION TO HEIGHTS AND DISTANCES. 

1. In every plane triangle there are six parts: three 
sides and three angles. These parts are so related to each 
other, that when one side and any two other parts are 
given, the remaining ones can be obtained, either by geo¬ 
metrical construction or by trigonometrical computation. 

2. Plane Trigonometry explains the methods of com¬ 
puting the unknown parts of a plane triangle, when a suf¬ 
ficient number of the six parts is given. 

8. For the purpose of trigonometrical calculation, the 
circumference of the circle is supposed to be divided into 
860 equal parts, called degrees; each degree is supposed 
to be divided into 60 equal parts, called minutes; and 
each minute into 60 equal parts, called seconds. 

Degrees, minutes, and seconds, are designated respec¬ 
tively, by the characters ° ' ". For example, ten degrees , 
eiqhteen minutes , and fourteen seconds , would be written 
10° 18' 14". 

4. If two lines be drawn through the centre of the 
circle, at right angles to each other, they will divide the 
circumference into four equal parts, of 90° each. Every 
right angle then, as EOA, is measured by an arc of 90°; 
every acute angle, as BOA , by an arc less than 90°; and 
every obtuse angle, as FOA, by an arc greater than 90°. 

5. The complement of an arc is 
what remains after subtracting the 
arc from 90°. Thus, the arc EB 
is the complement of AB. The 
sum of an arc and its complement 
is equal to 90°. 

6. The supplement of an arc is 
what remains after subtracting the 
arc from 180°. Thus, GF is the 













SEC. L] PLANE TRIGONOMETRY. 39 

supplement of the arc AEF. The sum of an arc and its 
supplement is equal to 180°. 

7. The sine of an arc is the perpendicular let fall from 
one extremity of the arc on the diameter which passes 
through the other extremity. Thus, BD is the sine of the 
arc AB. 

8. The cosine of an arc is the part of the diameter in¬ 
tercepted between the foot of the sine and centre. Thus, 
OB is the cosine of the arc AB. 

9. The tangent of an arc is the line which touches it at 
one extremity, and is limited by a line drawn through the 
other extremity and the centre of the circle. Thus, AO is 
the tangent of the arc AB. 

10. The secant of an arc is the line drawn from the 
centre of the circle through one extremity of the arc, and 
limited by the tangent passing through the other extremi¬ 
ty. Thus, 00 is the secant of the arc AB. 

11. The four lines, BD, OB , AC , 00, depend for their 
values on the arc AB and the radius OA; they are thus 
designated : 

sin AB for BD 
cos AB for OD 
tan AB for AO 
sec AB for 00 

12. If ABE be equal to a quadrant, or 90°, then EB 
will be the complement of AB. Let the lines ET and IB 
be drawn perpendicular to OE. Then, 

ET, the tangent of EB , is called the cotangent of AB; 

IB, the sine of EB, is equal to the cosine of AB; 

OT,\ the secant of EB, is called the cosecant of AB. 

In general, if A is any arc or angle, we have, 

cos A = sin (90° — A) 
cot A = tan (90° — A) 
cosec A = sec (90° — A) 


40 


ELEMENTS OF SURVEYING. 


[BOOK I 


13. If we take an arc, ABEF\ 
greater than 90°, its sine will be 
FH; OH will be its cosine; AQ 
its tangent, and OQ its secant. 

But FH is the sine of the arc GF\ 
which is the supplement of AF 1 
and OH is its cosine; hence, the 
sine of an arc is equal to the sine of 
its supplement; and the cosine of an 
arc is equal to the cosine of its supplementA 

Furthermore, AQ is the tangent of the arc AF : and 
OQ is its secant: GL is the tangent, and OL the secant 
of the supplemental arc GF. But since AQ is equal to 
GL , and OQ to OL , it follows that, the tangent of an arc 
is equal to the tangent of its supplement; and the secant of an 
arc is equal to the secant of its supplement .* 

TABLE OF NATURAL SINES. 

14. Let us suppose, that in a circle of a given radius, 
the lengths of the sine, cosine, tangent, and cotangent, have 
been calculated for every minute or second of the quad¬ 
rant, and arranged in a table; such a table is called a 
table of sines and tangents. If the radius of the circle is 
1, the table is called a table of natural sines. A table of 
natural sines, therefore, shows the values of the sines, co¬ 
sines, tangents, and cotangents of all the arcs of a quad¬ 
rant, which is divided to minutes or seconds. 

If the sines, cosines, tangents, and secants are known 
for arcs less than 90°, those for arcs which are greater can 
be found from them. For if an arc is less than 90°, its 
supplement will be greater than 90°, and the numerical 
values of these lines are the same for an arc and its sup¬ 
plement. Thus, if we know the sine of 20°, we also know 
the sine of its supplement 160°; for the two are equal to 
each other. The Table of Natural Sines, beginning at page 
63, of the tables shows the values of the sines and cosines 
only. 



* These relations are between the numerical values of the trigonometrieal lines; 
the algebraic signs, which they have in the different quadrants, are not considered. 












SEC. III.] 


PLANE TRIGONOMETRY. 


41 


TABLE OF LOGARITHMIC SINES. 

15. In this table are arranged the logarithms of the 
numerical values of the sines, cosines, tangents, and co¬ 
tangents of all the arcs of a quadrant, calculated to a ra¬ 
dius of 10,000,000,000. The logarithm of this radius is 10. 
In the first and last horizontal lines of each page, are writ¬ 
ten the degrees whose sines, cosines, &c., are expressed on 
the page. The vertical columns on the left and right, are 
columns of minutes. 


CASE I. 

To find, in the table , the logarithmic sine, cosine, tangent , or 
cotangent of any given arc or angle . 

16. If the angle is less than 45°, look for the degrees 
m the first horizontal line of the different pages: when the 
degrees are found, descend along the column of minutes, on 
the left of the page, till you reach the number showing the 
minutes : then pass along a horizontal line till you come into 
the column designated, sine, cosine, tangent, or cotangent, as 
the case may be: the number so indicated is the logarithm 
sought. Thus, on page 37, for 19° 55', we find, 

sine 19° 55' ... . 9.532312 

cos 19° 55' ... . 9.973215 

tan 19° 55' ... . 9.559097 

cot 19° 55' ... . 10.440903 

17. If the angle is greater than 45°, search for the de¬ 
grees along the bottom line of the different pages : when the 
number is found, ascend along the column of minutes on the 
right hand side of the page, till you reach the number express¬ 
ing the minutes: then pass along a horizontal line into the 
column designated tang, cot, sine, or cosine, as the case may 
be: the number so pointed out is the logarithm required. 

18. The column designated sine, at the top of the page, 
is designated by cosine at the bottom; the one designated 
tang, by cotang, and the one designated cotang, by tang. 

The angle found by taking the degrees at the top of 
the page, and the minutes from the left hand vertical column, 
is the complement of the angle found by taking the degrees 


42 


ELEMENTS OF SURVEYING. 


[BOOK I. 


at the bottom of the page, and the minutes from the right 
hand column on the same horizontal line with the first. 
Therefore, sine, at the top of the page, should correspond 
with cosine, at the bottom; cosine with sine, tang with 
cotang, and cotang with tang, as in the tables (Art. 12). 

If the angle is greater than 90°, we have only to sub¬ 
tract it from 180°, and take the sine, cosine, tangent, or 
cotangent of the remainder. 

The column of the table next to the column of sines, 
and on the right of it, is designated by the letter D. 
This column is calculated in the following manner. 

Opening the table at any page, as 42, the sine of 24° 
is found to be 9.609313; that of 24° 01', 9.609597: their 
difference is 284; this being divided by 60, the number 
of seconds in a minute, gives 4.73, which is entered in the 
column D. 

Now, supposing the increase of the logarithmic sine to 
be proportional to the increase of the arc, and it is nearly 
so for 60", it follows, that 4.73 is the increase of the sine 
for 1". Similarly, if the. arc were 24° 20', the increase of 
the sine for 1", would be 4.65. 

The same remarks are applicable in respect of the 
column D , after the column cosine, and of the column 
between the tangents and cotangents. The column D , be¬ 
tween the columns tangents and cotangents, answers to 
both of these columns. 

Now, if it were required to find the logarithmic sine 
of an arc expressed in degrees, minutes, and seconds, we 
have only to find the degrees and minutes as before; then, 
multiply the corresponding tabular difference by the sec¬ 
onds, and add the product to the number first found, for 
the sine of the given arc. 

Thus, if we wish the sine of 40° 26' 28". 

# 

The sine 40° 26' . . . 9.811952 

Tabular difference 2.47 . 

Number of seconds 28 . 

Product, 69.16 to be added 69.16 

Gives for the sine of 40° 26' 28". 


9.812021. 





SEC. Ill] 


PLANE TRIGONOMETRY. 


43 


4 

The decimal figures at the right are generally omitted 
in the last result; but when they exceed five-tenths, the 
figure on the left of the decimal point is increased by 1; 
the logarithm obtained is then exact, to within less than 
one unit of its right hand place. 

The tangent of an arc, in which there are seconds, is 
found in a manner entirely similar. In regard to the co¬ 
sine and cotangent, it must be remembered, that they in¬ 
crease while the arcs decrease, and decrease as the arcs are 
increased; consequently, the proportional numbers found 
for the seconds, must be subtracted, not added. 

EXAMPLES. 

1. To find the cosine of 3° 40' 40". 

The cosine of 3° 40' . . . 9.999110 

i 

Tabular difference .13 . 

Number of seconds 40 

Product, 5.20 to be subtracted 5.20 

Gives for the cosine of 3° 40' 40" 9.999105. 

2. Find the tangent of 37° 28' 31". 

Ans. 9.884592. 

3. Find the cotangent of 87° 57' 59". 

-4.925. 8.550356. 

CASE II. 

To find the degrees, minutes , and seconds answering to any 
given logarithmic sine , cosine, tangent, or cotangent. 

19. Search in the table, in the proper column, and 
if the number is found, the degrees will be shown either 
at the top or bottom of the page, and the minutes in the 
side column either at the left or right. 

But, if the number cannot be found in the table, take 
from the table the degrees and minutes answering to the 
nearest less logarithm, the logarithm itself, and also the 
corresponding tabular difference. Subtract the logarithm 
taken from the table from the given logarithm, annex two 




44 


ELEMENTS OF SURVEYING. 


[BOOK I. 


ciphers to the remainder, and then divide the remainder 
by the tabular difference: the quotient will be seconds, 
and is to be connected with the degrees and minutes be¬ 
fore found: to be added for the sine and tangent, and 
subtracted for the cosine and cotangent. 


EXAMPLES. 

1. Find the arc answering to the sine 9.880054 
Sine 49° 20', next less in the table 9.879963 

Tabular difference, 1.81)91.00(50". 

Hence, the arc 49° 20' 50" corresponds to the given sine 
9.880054. 

2. Find the arc whose cotangent is 10.008688 
cot 44° 26', next less in the table 10.008591 

Tabular difference, 4.21)97.00(23". 

Hence, 44° 26' —23" = 44° 25' 37" is the arc answering 
to the given cotangent 10.008688. 

3. Find the arc answering to tangent 9.979110. 

Arts. 43° 37' 21". 

4. Find the arc answering to cosine 9.944599. 

Ans. 28° 19' 45". 

20. We shall now demonstrate the principal theorems 
of Plane Trigonometry. 


THEOREM I. 


The sides of a plane triangle are proportional to the sines of 

their opposite angles. 

21. Let ABC be a triangle; then will 

CB : CA : : sin A : sin B. 

For, with 1 as a centre, and AB 
equal to the less side BC\ as a ra¬ 
dius, describe the arc BI: and with 
B as a centre and the equal radius 71 El Ij F 
BC 1 describe the arc CL , and draw DE and CF ^perpen¬ 
dicular to AB: now DE is the sine of the angle A, and 









SEC. Ill] 


PLANE TRIGONOMETRY. 


45 


CF is the sine of B, to the same radius AD or BG. But 
by similar triangles, 

AD : DE : : AG : CF. 

But AD being equal to BC, we have 

BG : sin A : : AG : sin B, or 

BG : AC : : sin A : sin B. 

By comparing the sides AB, AG, in a similar manner, 
we should find, 

AB : AG : : sin C : sin B. 


tan ±(C—B). 



THEOREM II. 

In any triangle, the sum of the two sides containing either 
angle, is to their difference, as the tangent of half the sum of 
the two other angles, to the tangent of half their difference. 

22. Let A GB be a triangle: then will 
ABF AG : AB—AG : : tan IfCFB) 

With 1 as a centre, and a 
radius AC, the less of the two 
given sides, let the semicircumfe¬ 
rence IFGE be described, meeting 
AB in I, and BA produced, in F. 

Then, BE will be the sum of the C . . FGII 

sides, and BI their difference. Draw Cl and AF. 

Since CAE is an outward angle of the triangle A GB, 
it is equal to the sum of the inward angles G and B (Bk. 
I., Prop. XXV., Cor 6). But the angle GIE being at the 
circumference, is half the angle GAE at the centre (Bk. III., 
Prop. XVIII.); that is, half the sum of the angles G and 
B, or equal to 1{GFB). 

The angle AEC= ACB, is also equal to ABCF BAF; 
therefore, BAF= ACB- ABC. 

But, ICF=l(BAF) = -l(ACB-ABC), or i(G-B). 

With I and G as centres, and the common radius IG, 
let the arcs CD and IG be described, and draw the lines 
GE and III perpendicular to 10. The perpendicular GE 
will pass through E, the extremity of the diameter IE, 




46 


ELEMENTS OF SURVEYING. 


[BOOK L 


since the right angle ICE must be 
inscribed in a semicircle. 

But CE is the tangent of CIE 
— and III is the tan¬ 

gent of ICB—\{C—B), to the 
common radius Cl 



...... -'FG7T 


But since the lines CE and III are parallel, the tri¬ 
angles BHI and BCE are similar, and give the proportion, 


BE : BI : : CE : III , or 

by placing for BE and BI, CE and III, their values, we 
have 


AB-\-AC : AB—AC :: tan \{C+B) : tan \{C—B). 


THEOREM III. 

In any plane triangle , if a line is drawn from the vertical 
angle perpendicular to the base , dividing it into two segments: 
then , the whole base, or sum of the segments , is to the sum of 
the tivo other sides , as the difference of those sides to the differ¬ 
ence of the segments. 

23. Let BA C be a triangle, and AD perpendicular to the 
base; then will 

BC * CA + AB :: CA-AB : CD-DB. 

For, AB~ = Sir + Id" 

(Bk. IV., Prop. XI.); 

and AG~ — DC'' + AIT 

-o -2 

by subtraction, A C — AB~ — 

CD 2 - BD\ 

But since the difference of 
the squares of two lines is equivalent to the rectangle con¬ 
tained by their sum and difference (Bk. IV., Prop. X.), we 
have, 

ACT - AK = (. AC+ AB). (. AC- AB) 

and CTf - DB~ = (CD + DB).{CD-DB) 

therefore, {CD + DB).{CD- DB) — {AC+ AB ). {AC— AB) 
hence, CD + DB : AC+AB :: AC-AB : CD-DB. 


A. 



















. SEC. Ill] 


PLANE TRIGONOMETRY. 


47 


THEOREM IY. 

In any right-angled plane triangle , radius is to the tangent 
of either of the acute angles , as the side adjacent to the side 
opposite. 

24. Let CAB be the proposed triangle, and denote the 
radius by R: then will 

J5 

R : tan C : : AC : AB. 

For, with any radius as CD de¬ 
scribe the arc DII, and draw the tan¬ 
gent DC. 

From the similar triangles CDC and CAB , we have, 

CD : DC : : CA : AB ; hence, 

R : tan C : : CA : AB. 

By describing an arc with 5 as a centre, we could 
show in the same manner that, 

R : tan B : : AB : AC. 



THEOREM V. 

In every right-angled plane triangle , radius is to the cosine 
of either of the acute angles , as the hypothenuse to the side 
adjacent. 

25. Let ABC be a triangle, right-angled at B: then will, 
R : cos A : : AC : AB. 

For, from the point 4 as a centre, 
wi^h any radius as AD ) describe the 
arc DF\ which will measure the angle 
A, and draw DE perpendicular to AB: then will AE be 
the cosine of A. 

The triangles ADE and ACB , being similar, we have, 

r 

AD : AE : : AC : AB: that is, 

R : cos A : : AC : AB. 

Remark. The relations between the sides and angles 
of plane triangles, demonstrated in these five theorems, are 









48 


ELEMENTS OF SURVEYING. 


[BOOK I. 


sufficient to solve all the cases of Plane Trigonometry. 
Of the six parts which make up a plane triangle, three 
must be given, and at least one of these a side, before the 
others can be determined. 

If the three angles only are given, it is plain, that an 
indefinite number of similar triangles may be constructed, 
the angles of which shall be respectively equal to the 
angles that are given, and therefore, the sides could not be 
determined. 

Assuming, with this restriction, any three parts of a 
triangle as given, one of the four following cases will al¬ 
ways be presented. 

I. When two angles and a side are given. 

II. When two sides and an opposite angle are given. 

III. When two sides and the included angle are given. 

IV. When the three sides are given. 

CASE I. 

When two angles and a side are given. 

26. Add the given angles together, and subtract their 
sum from 180 degrees. The remaining parts of the tri¬ 
angle can then be found by Theorem I. 

9 

EXAMPLES. 

1. In a plane triangle, A BC 1 
there are given the angle A = 58° 07', 
the angle B= 22° 37', and the side 
AB= 408 yards. Required the oth¬ 
er parts. 

GEOMETRICALLY. 

27. Draw an indefinite straight line, AB, and from the 
scale of equal parts lay off AB equal to 408. Then, 
at A , lay off an angle equal to 58° 07', and at B an angle 
equal to 22° 37', and draw the lines AC and BC: then 
will ABC be the triangle required. 

The angle C may be measured either with the protractor 
or the scale of chords (Sec. II., Arts. 42 and 44), and will be 




SEC. Ill] 


PLANE TRIGONOMETRY. 


49 


found equal to 99° 16'. The sides AC and BC may be 
measured by referring them to the scale of equal parts 
(Sec. II., Art. 40). We shall find A0— 158.9 and BC— 351 
yards. 


TRIGONOMETRICALLY BY LOGARITHMS. 

To the angle ... A— 58° 07' 

Add the angle . . B — 22° 87' 

Their sum, = 80° 44' 

taken from . . . 180° 00' 

leaves C .... 99° 16', of which, as it ex¬ 

ceeds 90°, we use the supplement 80° 44'. 


To find the side BC. 


4 

sin C 99° 16' ar. comp. 0.005705 

: sin A 58° 07'. 9.928972 

: : AB 408 . 2.610660 


BC 851.024 (after rejecting 10) 2.545337. 

Remark. The logarithm of the fourth term of a pro¬ 
portion is obtained by adding the logarithm of the second 
term to that of the third, and subtracting from their sum 
the logarithm of the first term. But to subtract the first 
term is the same as to add its arithmetical complement 
and reject 10 from the sum (Sec. I., Art. 13): hence, the arith¬ 
metical complement of the first term added to the loga¬ 
rithms of the second and third terms, minus ten, will give 
the logarithm of the fourth term. 

To find the side AC. 


sin C 99° 16' ar. comp. 0.005705 

sin B 22° 37'. 9.584968 

: AB 408 . 2.610660 

AC 158.976 . 2.201333 


2. In a triangle ABC, there are given A = 38° 25', 
B=57° 42', and AB = 400: required the remaining parts. 

Ans. C= 83° 53', £0=249.974, AC= 340.04. 

4 














50 


ELEMENTS OF SURVEYING. 


[BOOK I. 


CASE II. 


When two sides and an opposite angle are given. 


28. In a plane triangle, ABC\ 
there are given AC— 216, CB = 117, 
the angle A — 22° 37', to find the 
other parts.. 


c 



GEOMETRICALLY. 

29. Draw an indefinite right line ABB' : from any 
point, as A, draw AC\ making BAC— 22° 37', and make 
AC =216. With C as a centre, and a radius equal to 117, 
the other given side, describe the arc B'B ; draw B'C and 
BC: then will either of the triangles ABC or AB' (7, an¬ 
swer all the conditions of the question. 

TRIGONOMETRICALLY. 


To find the angle B. 

BC 117 ar. comp. 7.931814 

AC 216 . 2.334454 

: sin A 22° 37'. 9.584968 


: sin B' 45° 13' 55", or ABC 134° 46' 05" 9.851236. 

The ambiguity in this, and similar examples, arises in 
consequence of the first' proportion being true for either 
of the angles ABC, or ABC, which are supplements of 
each other, and therefore, have the same sine (Art. 13). 
As long as the two triangles exist, the ambiguity will con¬ 
tinue. But if the side CB, opposite the given angle, is 
greater than A C, the arc BB will cut the line ABB', on 
the same side of the point A , in but one point, and then 
there will be only one triangle answering the conditions. 

If the side GB is equal to the perpendicular Cd , the 
rc BB will be tangent to ABB, and in this case also 
there will be but one triangle. When CB is less than the 
perpendicular Cd, the arc BB' will not intersect the base 
ABB, and in that case, no triangle can be formed, or it 
will be impossible to fulfil the conditions of the problem. 









SEC. Ill] 


PLANE TRIGONOMETRY. 


51 


2. Given two sides of a triangle 50 and 40 respectively, 
and the angle opposite the latter equal to 32° : required 
the remaining parts of the triangle. 

Ans. If the angle opposite the side 50 is acute, it is 
equal to 41° 28' 59"; the third angle is then equal to 
106° 31' 01", and the third side to 72.368. If the angle 
opposite the side 50 is obtuse, it is equal to 138° 31' 01", 
the third angle to 9° 28' 59", and the remaining side to 
12.436. 

CASE III. 


When tiuo sides and their included angle are given. 


30. Let ABO be a triangle; AB , 
BO\ the given sides, and B the 
given angle. 

Since B is known, we can find 
the sum of the two other angles: 
for 


A. 



A+0= 180° - B f and, 

¥A + 0) = 4(180° - B). 


We next find half the difference of the angles A and 
O by Theorem II., viz., 

BO A BA : BO—BA :: tan 4(H + @) : tan 4 (A—O), 

in which we consider BO greater than BA, and therefore 
A is greater than 0\ since the greater angle must be op¬ 
posite the greater side. 

Saving found half the difference of A and O, by add¬ 
ing it to the half sum, \(A + 0), we obtain the greater 
angle, and by subtracting it from half the sum, we obtain 
the less. That is, 

4 {A + 0) A \(A — 0) = A, and 
-K AA-0)-i(A-0)=0 

Having found the angles A and C.\ the third side AO 
may be found by the proportion, 

sin A : sin B : : BO : AO. 



52 


ELEMENTS OF SURVEYING. 


[BOOK L 


EXAMPLES. 

1. In the triangle ABO, let 15(7=540, HI? = 450, and 
the included angle B = 80°: required the remaining parts. 

GEOMETRICALLY. 

31. Draw an indefinite right line BO, and from any 
point, as B, lay off a distance BC =540. At B make the 
angle CBA = 80° : draw BA, and make the distance 
BA = 450 ; draw A G ; then will AB 0 be the required tri¬ 
angle. 

TRIGONOMETRICALLY. 

BO 4- BA — 540 + 450 = 990; and BO-BA = 540 - 450 = 90. 
A. + O— 180° — B — 180° — 80° = 100°, and therefore, 
J(A+(7) = i(100 o ) = 50 o . 


To find \(A — C). 

BG-\-BA 990 ar. comp. 7.004365 

BO- BA 90 . 1.954243 

: tan ^(A + O) 50°. 10.076187 

tan |(A -O) 6° 11'. 9.034795. 


Hence, 50° + 6° 11' = 56° 11' = A; and 50° — 6° 11' = 
43° 49' = O 

To find the third side AC. 


sin O 43° 49' ar comp. 0.159672 

: sin B 80° . 9.993351 

• : AB 450 . 2.653213 


AO 640.082 . 2.806236. 


2. Given two sides of a plane triangle, 1686 and 960, 
and their included angle 128° 04': required the other parts. 

Ans. Angles, 33° 34' 39"; 18° 21' 21"; side 2400. 

% 

CASE IV. 

32. Having given the three sides of a plane triangle, 
to find the angles. 













PLANE TRIGONOMETRY. 


53 


SEC. III.] 

Let fall a perpendicular from the angle opposite the 
greater side, dividing the given triangle into two right- 
angled triangles: then find the difference of the segments 
of the base by Theorem III. Half this difference being 
added to half the base, gives the greater segment; and, 
being subtracted from half the base, gives the less segment. 
Then, since the greater segment belongs to the right-angled 
triangle having the greater hypothenuse, we have two 
sides and the right angle of each- of two right-angled tri¬ 
angles, to find the acute angles. 

EXAMPLES. 

A 

1. The sides of a plane triangle 
being given ; viz., BC= 40, A 0= 34, 
and AB = 25 : required the angles. 



GEOMETRICALLY. 

33. With the three given lines as sides construct a tri¬ 
angle as in Prob. IX. Then measure the angles of the 
triangle either with the protractor or scale of chords. 

TRIGONOMETRICALLY. 

BG : AC+AB :: AC - AB : CD-BD , 

That is, 40 : 59 : : 9 : = 13.275. 

’ 40 

Then, 40 + 43 ' 275 = 26.6375 = CD, 

And, 40 ~ = 13.3625 = BD. 

u 

In the triangle DAG , to find the angle DAG. 


AG 34 ar. comp.* 8.468521 

: DG 26.6375 . 1.425493 

: : sin D 90°. 10.000000 

: sin DAG 51° 34' 40". 9.894014. 












54 


ELEMENTS OF SURVEYING. 


[BOOK I. 


In the triangle BAD , to find the angle BAD . 


AB 25 ar. comp. 8.602060 

BD 13.3625 1.125887 

: sin D 90°. 10.000000 

sin BAD 32° 18' 35". 9.727947. 


Hence, 90° - DAG= 90° - 51° 34' 40" = 38° 25' 20" = 0,\ 
and, 90° - BAD = 90° - 32° 18' 35" = 57° 41' 25" = B, 
and, BAD + DAG =51° 34'40"+ 32° 18' 35" = 83° 53' 

15" = A. 

2. In a triangle, of which the sides are 4, 5, and 6, 
what are the angles? 

Ans. 41° 24' 35"; 55° 46' 16"; and 82° 49' 09". 


SOLUTION OF RIGHT-ANGLED TRIANGLES. 

34. The unknown parts of a right-angled triangle may 
be found by either of the four last cases; or, if two of the 
sides are given, by means of the property that the square 
of the hypothenuse is equivalent to the sum of the squares 
of the two other sides. Or the parts may be found by 
Theorems IY. and Y. 

EXAMPLES. 

1. In a right-angled triangle 
BACy there are given the hypothe¬ 
nuse BG= 250, and the base AG= 

240: required the other parts. 

To find the angle B. 


BO 250 ar. comp. 7.602060 

AC 240 . 2.380211 

: sin A 90° . . 10.000000 

sin B 73° 44' 23". 9.982271. 



But G— 90° - j?= 90° - 73° 44' 23" = 16° 15' 37": 
















S SC. Ill] PLANE TRIGONOMETRY. 55 

Or C may be found from the proportion. 

CB 350 ar. comp. 7.602060 

: AC 240 . 2.380211 

: : R . 10.000000 

: cos C 16° 15' 37". 9.982271. 


To find side AB by Theorem IV. 

R ar. comp. 0.000000 

: tan C 16° 15' 37". 9.464889 

: : AC 240 2.380211 

: AB 70.0003 . 1.845100. 


2. In a right-angled triangle BAG\ there are given 
4.(7=384, and 5=53° 08': required the remaining parts. 
Ans. 41? =287.96; .5(7=479.979; (7= 36° 52'. 

APPLICATION TO HEIGHTS AND DISTANCES. 


I. To determine the horizontal distance to a point which is in¬ 
accessible by reason of an intervening river A 

35. Let C be the point. Measure 
along the bank of the river a hori¬ 
zontal base line 45, and seject the 
stations 4 and 5, in such a man¬ 
ner that each can be seen from the 
other, and the point C from both 
of them. Then measure the hori¬ 
zontal angles CAB and 654, with 
an instrument adapted to that purpose. 

Let us suppose that we have found 45 = 600 yards, 
645 = 57° 35', and 654 = 64° 51'. 

The angle 6= 180° - (4 + 5) = 57° 34'. 

To find the distance BC. 


sin 6 57° 34' ar. comp. 0.073649 

: sin 4 57° 35'. 9.926431 

: : 45 600 . 2.778151 

: 56 600.11 yards .. 2.778231. 



* Read, definitions, from 3 to 14, pages 64 and 65. 

































56 


ELEMENTS OF SURVEYING. 


[BOOK L 


To find the distance AO. 


sin 0 57° 34' ar. comp. 0.073649 

sin B 64° 51'. 9.956744 

: AB 600 2.778151 

AG 643.94 yards. 2.808544. 


II. To determine the altitude of an inaccessible object above a 

given horizontal plane. 

FIRST METHOD. 

36. Suppose D to be the inac¬ 
cessible object, and BG the hori¬ 
zontal plane from which the alti¬ 
tude is to be estimated: then, if 
we suppose BG to be a vertical 
line, it will represent the required 
distance. 

Measure any horizontal base line, as BA ; and at the 
extremities B and A, measure the horizontal angles GBA 
and GAB. Measure also the angle of elevation DBG. 

Then in the triangle GBA there will be known, two 
angles and the side AB ; the *side BO can therefore be 
determined. Having found BG\ we shall have, in the 
right-angled triangle BBG, the base BG and the angle at 
the base, to find the perpendicular DO\ which measures 
the altitude of the point D above the horizontal plane BG. 

Let us suppose that we have found 

iM = 780 yards, the horizontal angle CBA = 4A° 24'; 
the horizontal angle GAB= 96° 28', and the angle of eleva¬ 
tion DBG =10° 4:3'. 

In the triangle BOA, to find the horizontal distance BG. 
The angle BOA = 180° - (41° 24' + 96° 28') = 42° 08' = G. 


sin G 42° 08' ar. comp. 0.173369 

sin A 96° 28'. 9.997228 

: AB 780 . 2.892095 


BG 1155.29 . 3.062699 


D 















SEO. Ill] 


PLANE TRIGONOMETRY. 


57 


In the right-angled triangle DEC\ to find DC. 


R ar. comp. 0.000000 

tan DBG 10° 43'. 9.277043 

EG 1155.29 3.062692 

DC 218.64 2.339735. 


Remark I. It might, at first, appear, that the solution 
which we have given, requires that the points E and A 
should be in the same horizontal plane; but it is entirely 
independent of such a supposition. 

For, the horizontal distance, which is represented by 
EA , is the same, whether the station A is on the same 
level with E, above it, or below it. The horizontal angles 
GAB and GEA are also the same, so long as the point G 
is in the vertical line DG. Therefore, if the horizontal 
line through A should cut the vertical line DC\ at any 
point, as E , above or below G, AB would still be the hori¬ 
zontal distance between E and A, and AE\ which is equal 
to A C , would be the horizontal distance betw.een A and G. 

If at A, we measure the angle of elevation of the point 
D, we shall know in the right-angled triangle DAE\ the 
base AE, and the angle at the base; from which the per¬ 
pendicular DE can be determined. 

37. Let us suppose that we had measured the angle of 
elevation DAE\ and found it equal to 20° 15'. 

First: In the triangle BAG, to find AG or its equal AE. 


sin G 42° 08' ar. comp. 0.173369 

sin E 41° 24'. 9.820406 

: AB 780 2.892095 

AG 768.9 2.885870. 


In the right-angled triangle DAE, to find DE. 

R ar. comp. 0.000000 

tan A 20° 15'. 9.566932 

AE 768.9 . 2.885870 

DE 283.66 . 2.452802. 




















58 ELEMENTS OF SURVEYING. [BOOK! 

Now, since BC is less than 
BE\ it follows that the station B 
is above the station A. * That is, 

BE- DC= 283.66 - 218.64 = 

65.02 = EG ,; 

which expresses the vertical dis¬ 
tance that the station B is above 
the station A. 

Kemark II. It should be remembered, that the vertical 
distance which is obtained by the calculation, is estimated 
from a horizontal line passing through the eye at the time 
of observation. Hence, the height of the instrument is to 
be added, in order to obtain the true result. 



SECOND METHOD. 

38. When the nature of the ground will admit of it, 
measure a base line AB in the direction of the object B. 
Then measure with the instrument the angles of elevation 
at A and B. 

Then, since the out¬ 
ward angle BBC is 
equal to the sum of 
the angles A and ABB , 
it follows that the an¬ 
gle ABB is equal to the difference of the angles of eleva¬ 
tion at A and B. Hence, we can find all the parts of the 
triangle ABB. Having found BB, and knowing the angle 
BBC\ we can find the altitude BC. 

This method supposes that the stations A and B are on 
the same horizontal plane; and therefore it can only be 
used when the line AB is nearly horizontal. 

Let us suppose that we have measured the base line, 
and the two angles of elevation, and 



found 


AB 

A 

BBC 


975 yards, 
15° 36', 

27° 29'; 


required the altitude BC. 








SEC. IIL] 


PLANE TRIGONOMETRY. 


59 


First: ABB— BBC - A = 27° 29' -15° 36' = 11° 53'. 
In the triangle ABB\ to find BB. 


sin B 11° 53' ar. comp. 0.686302 

sin A 15° 36'. 9.429623 

AB 975 2.989005 

BB 1273.3 3.104930. 


. In the triangle BBC\ to find BC. 


B ar. comp. 0.000000 

sin B 27° 29'. 9.664163 

BB 1273.3 3.104930 

BC 587.61 2.769093. 


III. To determine the perpendicular distance of an object below 

a given horizontal plane. 

39. Suppose C to be directly 
over the given object, and A the 
point through which the horizon¬ 
tal plane is supposed to pass. 

Measure a horizontal base line 
AB, and at the stations A and 
B conceive the two horizontal 
lines AC, BC, to be drawn. The 
oblique lines from A and B to the object are the hy- 
pothenuses of two right-angled triangles, of which AC, BC, 
are the bases. The perpendiculars of these triangles are 
the distances from the horizontal lines AC, BC, to the 
object. If we turn the triangles about their bases AC, 
BC, until they become horizontal, the object, in the first 
case, will fall at C, and in the second at C". 

Measure the horizontal angles CAB, CBA, and also the 
angles of depression C'AC, C"BC. 


















60 


ELEMENTS OF SURVEYING. 


[BOOK I. 


Let us suppose that we have 


found 


-< 


AB = 672 yards 
BAC = 72° 29' 
ABC = 39° 20' 

O'AC = 27° 49' 


C"BG — 19° 10'. 


First: in the triangle ABC, 

■»the horizontal angle A CB = 180° — (A + B) = 180° — 111° 
49' = 68° IF. 


To find the horizontal distance AC. 


sin C 68° 11' ar. comp. 0.032275 

sin B 39° 20'. 9.801973 

AB 672 2.827369 

AC 458.79 2.661617. 


To find the horizontal distance BC. 


sin C 68° 11' ar. comp. 0.032275 

: sin A 72° 29' .. 9.979380 

:: AB 672 . 2.827369 

BC 690.28 . 2.839024. 


In the triangle CAC', to find CC'. 


R ar. comp. 0.000000 

tan CAC 27° 49'. 9.722315 

AC 458.79 2.661617 

CC ' 242.06 2.383932. 


In the triangle CBC ", to find CC". 


R ar. comp. 0.000000 

: tan C"BC 19° 10'. 9.541061 

: : BC 690.28 2.839024 

: CC" 239.93 2.380085. 


Hence also, CC' — CC" = 242.06 — 239.93 = 2.13 yards, 
which is the height of the station A above station B. 

























SEC. III.] 


PLANE TRIGONOMETRY. 


61 


PROBLEMS. 

1. Wanting to know the distance between two inacces¬ 
sible objects, which lie in a direct level line from the bot¬ 
tom of a tower of 120 feet in height, the angles of depres¬ 
sion are measured from the top of the tower, and are found 
to be, of the nearer 57°, of the more remote 25° 30': re¬ 
quired the distance between the objects. 

2. In order to find the distance 
between two trees, A and i?, which 
could not be directly measured be¬ 
cause of a pool which occupied -the 
intermediate space, the distances 
of a third point G from each of 
them were measured, and also the 
included angle AGB : it was found that, 

CB = 672 yards, 

GA = 588 yards, 

AGB = 55° 40'; 

required the distance AB. Ans. 592.967 yards. 

3. Being on a horizontal plane, and wanting to ascer¬ 
tain the height of a tower, standing on the top of an in¬ 
accessible hill, there were measured, the angle of elevation 
of the top of the hill 40°, and of the top of the tower 51°; 
then measuring in a direct line 180 feet farther from the 
hill, the angle of elevation of the top of the tower was 
33° 45'; required the height of the tower. 

Ans. 83.998. 


Am. 173.656 feet. 



4. Wanting to know the hori¬ 
zontal distance between two inac¬ 
cessible objects E and TFJ the fol¬ 
lowing measurements were made. 


AB = 536 yards 
BA W = 40° 16' 
viz. WAE=57° 40' 
ABE = 42° 22' 
^EBW = 71° 07'; 
required the distance EW. 



Ans. 939.527 yards. 




















62 


ELEMENTS OF SURVEYING. 


[BOOK I 


5. Wanting to know the 
horizontal distance between 
two inacessible objects A 
and B, and not finding any 
station from which both of 
them could be seen, two 
points G and D, were chosen 
at a distance from each other, equal to 200 yards; from 
the former of these points A could be seen, and from the 
latter B , and at each of the points C and D a staff was 
set up. From C a distance OF was measured, not in the 
direction DC, equal to 200 yards, and from D a distance 
DE equal to 200 yards, and the following angles taken, 

f AFC = 83° 00', BDE= 54° 30', 
viz. \ A CD = 53° 30', BDC = 156° 25', 

[ AGF = 54° 31', BED = 88° 80'. 

Ans. AB — 345.467 yards. 



6. From a station P there 
can be seen three objects, A, 

B and C, whose distances from 
each other are known: viz., 
A3= 800, AC=600 , and BC 
— 400 yards. ISTow, there are 
measured the horizontal an- 
gles. 

APO= 83° 45' and BPO 
= 22° 30': it is required to 
find the three distances PA, PC, 



and PB. 


PA = 710.193 yards. 
Ans. \ PC = 1042.522 
PB = 934.291. 


% 


7. This problem is much used in maritime survey¬ 
ing, for the purpose of locating buoys and sounding boats. 
The trigonometrical solution is somewhat tedious, but it 
may be solved geometrically by the following easv con¬ 
struction. 






SEC. Ill] PLANE TRIGONOMETRY. 68 

• Let A , B, and G be the 
three fixed points on shore, 
and P the position of the 
boat from which the angles 
APG= 33° 45', GPB= 22° 30', 
and APB = 56° 15', have been 
measured. 

Subtract twice APG=67° 

30' from 180°, and lay off at 
A and G two angles, GA 0, 

AGO, each equal to half the 
remainder =56° 15'. With 
the point 0, thus determined, 
as a centre, and OA or OG as a radius, describe the cir¬ 
cumference of a circle: then, any angle inscribed in the 
segment APC\ will be equal to 33° 45'. 

Subtract, in like manner, twice OPS =45°, from 180°, 
and lay off half the remainder = 67° 30', at B and (7, de¬ 
termining the centre Q of a second circle, upon the cir¬ 
cumference of which the point P will be found. The 
required point P will be at the intersection of these two 
circumferences. If the point P fall on the circumference 
described through the' three points A, B , and 0\ the two 
auxiliary circles will coincide, and the problem will be in¬ 
determinate. 






BOOK II. 

PLANE SURVEYING. 


i {, , - 

SECTION I. 

DEFINITIONS.—MEASUREMENT OF ANGLES AND LINES. 

1. Surveying, in its most extensive signification, com¬ 
prises all the operations necessary for finding, 

1st. The area or contents of any portion of the surface 
of the earth; 

2d. The lengths and directions of the bounding lines; 
and, 

3d. For making accurate delineations of the surface and 
bounding lines on paper. 

It is divided into two branches, Plane and Geodesic . 
Surveying. 

2. The' radius of the earth being very large, the curva¬ 
ture may be neglected, when the survey is limited to small 
portions of the surface. This branch is called Plane Sur¬ 
veying. 

When the curvature is taken into account, as it must 
be in all extensive surveys, the method of measurement 
and computation is called Geodesic Surveying. 

3. If at any point of the surface of the earth, regarded 
as a sphere, a plane be passed perpendicular to the radius, 
it will be tangent to the surface. Such a plane, and all 
planes parallel to it, are called horizontal planes. 

4. A plane perpendicular to a horizontal plane, at a 
given point, is called a vertical plane. 



SEC. I] 


DEFINITIONS. 


65 


5. All lines of horizontal planes are called horizontal 
lines. 

6. Lines which are perpendicular to a horizontal plane, 
are called vertical lines; and all lines which are inclined to 
it, are called oblique lines. 

Thus, AB and DC are hori¬ 
zontal lines; BG and AD are 
vertical lines; and A C and BD 
are oblique lines. 

7. The horizontal distance 
between two points, is the horizontal line intercepted be¬ 
tween the two vertical lines passing through those points. 
Thus, DC or AB is the horizontal distance between the two 
points A and C\ or the points B and D. 

8. A horizontal angle is one whose sides are horizontal; 
its plane is also horizontal. 

A horizontal angle may also be defined to be, the angle 
included between two verticcd planes passing through the angular 
point, and the two objects ivhicli subtend the angle. 

4 

9. A vertical angle is one, the plane of whose sides is 
vertical. 

10. An angle of elevation , is a vertical angle having one 
of its sides horizontal, and the inclined side above the hor¬ 
izontal side. 

Thus, in the last figure, BAC is the angle of elevation 
from A to G. 

« 

11. An angle of depression , is a vertical angle having 
one of its sides horizontal, and the inclined side under the 
horizontal side. Thus, DC A is the angle of depression 
from G to A. 

12. An oblique angle is one, the plane of whose sides is 
oblique to a horizontal plane. 

13. All lines, which can be the object of measurement, 
must belong to one of the classes above named, viz.: 

1st. Horizontal lines: 

2d. Vertical lines: 

3d. Oblique lines. 




5 




66 


ELEMENTS OF SURVEYING. [BOOK II. 


14. All the angles may also be divided into three 
classes, viz.: 

% 

1st. Horizontal angles: 

2d. Vertical angles; which include angles of elevation 
and angles of depression,: and 

3d. Oblique angles, or those included by oblique lines. 


OF THE MEASUREMENT OF LINES AND ANGLES. 

15. It has been shown (Bk. I., Sec. III., Art. 1), that at 
least one side and two of the other parts of a plane triangle 
must be given or known, before the remaining parts can 
be found by calculation. 

When, therefore, distances are to be found, by trigono¬ 
metrical calculations, two preliminary steps are necessary: 

1st. To measure certain lines on the ground: 

2d. To measure such angles as may be necessary to de¬ 
termine the required parts. 


MEASURES FOR DISTANCES. 

16. Any tape, rod, or chain, divided into equal parts, 
may be used as a measure; and one of these equal parts 
is called the unit of the measure. The unit of a measure 
may be a foot, a yard, a rod, or any other ascertained 
distance. 

The measure in general use, is a chain of four rods or 
sixty-six feet in length; it is called Gunter's chain, from 
the name of the inventor. This chain is composed of 100 
links. Every tenth link from either end, is marked by a 
small attached brass plate, which is notched, to designate 
its number from the end. The division of the chain into 
100 equal parts, is a very convenient one, since the divi¬ 
sions or links are decimals of the whole chain, and in the 
calculations may be treated as such. 


SEC. I] MEASUREMENT OF DISTANCES. 


67 


TABLE. 

1 chain = 4 rods =66 feet = 792 inches = 100 links. 
Hence, 1 link is equal to 7.92 inches. 

80 chains = 820 rods = l mile. 

40 chains = \ mile. 

20 chains = J mile. 

17. Besides the chain, there are needed for measuring, 
ten marking pins, which should he of iron, each about ten 
inches in length and an eighth of an inch in thickness. 
These pins should be strung upon an iron ring, and this 
ring should be attached to a belt, to be passed over the 
right shoulder, suspending the pins at the left side. Two 
staves are also required. Each of these should be about six 
feet in length, and have a spike in the lower end to aid in 
holding it firmly, and a horizontal strip of iron to pre¬ 
vent the chain from slipping off; these staves are to be 
passed through the rings at the ends of the chain. 

TO MEASURE A HORIZONTAL LINE. 

18. At the point where the measurement is to be be¬ 
gun, place, in a vertical position, a signal staff, having a 
small flag attached to its upper extremity; and place an¬ 
other at the point where the measurement is to be termi¬ 
nated. These two points are generally called stations. 

Having passed the staves through ‘the rings of the 
chain, let the ten marking pins and one end of the chain 
be taken by the person who is to go forward, and who is 
called the leader, and let him plant the staff as nearly as 
possible in the direction of the stations. Then, taking the 
staff in his right hand, let him stand off at arm’s length, 
so that the person at the other end of the chain can align 
it exactly with the stations: when the alignment is made, 
let the chain be stretched and a marking pin placed; then 
measure a second chain in the same manner, and so on, 
until all the marking pins shall have been placed. When 
the marking pins are exhausted, a note should be made, 
that ten chains have been measured; after which, the 
marking pins are to be returned to the leader, and the 


68 


ELEMENTS OF SURVEYING. [BOOK IL 


measurement continued as before, until the whole distance 
is passed over. It will be found desirable to fasten pieces 
of red cloth to the heads of the marking pins, that they 
may be more readily found in thick grass, brushwood, &c. 

Great care must be taken to keep the chain horizontal, 
and if the slope of the ground be too great to admit of 
measuring a whole chain at a time, a part of a chain only 
should be measured: the sum of all the horizontal lines so 
measured, is evidently the horizontal distance between the 
stations. 

For example, in measuring 
the horizontal distance between 
A and 0, we first place a staff 
at A and another at b, in the 
direction towards 0. Then 
slide up the chain on the staff 
at A until it becomes horizon¬ 
tal, and note the distance ab. 

Then remove the staves and place them at b and d: make 
the chain horizontal, and note the distance cd. Measure 
in the same manner the line fC ; the sum of the horizontal 
lines ab , cc?, fC\ is equal to AB , the horizontal distance be¬ 
tween A and C. 

19. The length of the chain should be compared, from 
time to time, with a standard kept for the purpose. 

To facilitate this comparison, let two stakes be driven 
in the ground, distant from each other one chain , and let 
nails be driven in the heads of the stakes to mark the ex 
act length of the standard. 

Marks made upon the coping of a wall will answer the 
same purpose. If it is- found that any line has been mea¬ 
sured with a chain, either too short or too long, the mea¬ 
sured distance may be corrected by the following pro¬ 
portion: 

As the length of the chain 

: the length of the standard 

: : the measured distance 

: the true distance. 












SEC. I] 


OF THE THEODOLITE. 


69 


For tlie correction of areas we have this proportion, 

As the square of the length of the chain 

: the square of the length of the standard, 

: : the area found 

: the area required. 

MEASUREMENT OF ANGLES. 

* 

20. We come now to the measurement of angles, and 
for this purpose several instruments are used. The one, 
however, which affords the most accurate results, and which 
indeed can alone be relied on for nice or extensive opera¬ 
tions, is called a Theodolite. This instrument only will be 
described at present; others will be subsequently explained. 


OF THE THEODOLITE. 

PI. 1. The theodolite is an instrument used to measure 
horizontal and vertical angles. It is usually placed on a 
tripod ABC, which enters by means'of a screw the lower 
horizontal plate DE) and becomes firmly attached to the 
body of the instrument. Through the horizontal plate DE, 
four small hollow cylinders are inserted, which receive 
four screws with milled heads, that work against a second 
horizontal plate, FG. The upper side of the plate DE 
terminates in a curved surface, which encompasses a ball, 
that is nearly a semi-sphere, with the plane of its base 
horizontal. This ball, which is hollow, is firmly connected 
with the smaller base of a hollow conic frustum, that 
passes through the curved part of the plate DE, and 
screws firmly into the curved part of the second horizontal 
plate FG. 

A hollow conic spindle passes through the middle of 
the ball, and the hollow frustum with which it is connect¬ 
ed. To this spindle, a third horizontal and circular plate 
HI, called the limb of the instrument, is permanently attached. 
Within this spindle, and concentric with it, there is a sec¬ 
ond spindle, called the inner, or solid spindle. To this 
latter, is united a thin circular plate, called the vernier plate. 



70 


ELEMENTS OF SURVEYING. [BOOK IL 


which, rests on the limb of the instrument, and supports 
the upper frame-work. The two spindles terminate at the 
base of the spherical ball, where a small screw enters the 
inner one, and presses a washer against the other, and the 
base of the ball. On the upper surface of the plate FG\ 
rests a clamp which goes round the outer spindle, and 
which, being compressed by the clamp-screw K, is made 
fast to it. This clamp is thus connected with the plate 
FG. A small' cylinder a, is fastened to the plate FG : 
through this cylinder a thumb-screw L passes, and works 
into a small cylinder 5, connected with the clamp. The 
cylinders b and a, admit of a motion round their axes, to 
relieve the screw L of the pressure which would otherwise 
be occasioned by working it. 

Directly above the clamp, is the lower telescope MN. 
This telescope is connected with a hollow cylinder, which 
is worked freely round the outer spindle, by the thumb¬ 
screw P having a pinion working into a concealed cog¬ 
wheel, that is permanently fastened to the limb of the in¬ 
strument. By means of a clamp-screw Q , the telescope is 
made fast to the limb, when it will have a common motion 
with the limb and outer spindle. 

The circular edge of the limb is chamfered, and is gen¬ 
erally made of silver, and on this circle the graduation for 
horizontal angles is made. In the instrument described, 
the circle is cut into degrees and half degrees; the degrees 
are numbered from 0 to 360. 

On the circular edge of the vernier plate, is a small 
plate of silver, called a vernier; this plate is divided into 
30 equal parts, and numbered from the line marked 0 to 
the left. Two levels, at right angles to each other, are 
attached to the vernier plate by small adjusting screws; 
one of the levels is seen in the figure. 

The vernier plate turns freely around with the inner 
spindle. It is made fast to the limb of the instrument by 
the clamp-screw A; after which the smaller motions are 
made by the tangent-screw T. There is a compass on the 
vernier plate, that is concentric with it, the use of which 
will be explained under the head compass. 


SEC. I] 


OF THE THEODOLITE. 


71 


The frame-work which supports the horizontal axis of 
the vertical semicircle UV and the upper telescope, with 
its attached level, rests on the vernier plate, to which it 
is made fast by three adjusting screws, placed at the angu¬ 
lar points of an equilateral triangle. The vertical semi¬ 
circle UV, is called the vertical limb ; its motions are gov¬ 
erned by the thumb-screw Z, which has a pinion, that 
works with the teeth of the vertical limb. On the face 
of the vertical limb, opposite the tliumb-screw Z, the limb 
is divided into degrees and half degrees: the degrees are 
numbered both ways from the line marked 0. There is a 
small plate resting against the graduated face of the verti¬ 
cal limb, called the vernier; it is divided into 30 equal 
parts, and the middle line is designated by 0. 

On the other face of the vertical limb, are two ranges 
of divisions, commencing at the 0 point, and extending 
each way 45°. The one shows the vertical distance of 
any object to which the upper telescope is directed, above 
or below the place of the instrument, in 100th parts of the 
horizontal distance: the other, the difference between the 
hypothenusal and base lines: the hypothenuse being sup¬ 
posed to be divided into one hundred equal parts: there¬ 
fore, by mere inspection, we can ascertain the number of 
links, which must be subtracted from everv chain of an 
oblique line, to reduce it to a true horizontal distance. 

The supports of the upper telescope are called the 
wyes, and designated Y’s. Two loops, turning on hinges, 
pass over the telescope, and are made fast by the pins c 
and d\ these loops confine the telescope in the Y's. By 
withdrawing the pins, and turning the loops on their 
hinges, the telescope may be removed for the purpose of 
being reversed in position; and in both situations, the tele¬ 
scope can be revolved in the Y’s about its axis. 

In the telescopes attached to the theodolite, are two 
principal lenses, one at each end. The one at the end 
where the eye is julaced, is called the eye-glass, the other 
the object-glass. 

In order that the axis of the telescope may be directed 
to an object with precision, two spider’s lines, or small 


72 


ELEMENTS OF SURVEYING. 


[BOOK IL 


hairs, are fixed at right angles to each other, and placed 
within the barrel of the telescope, and at the focus of the 
eye-glass. The vertical hair is moved by two small hori- * 
zontal screws, one of which, f is seen in the figure; and 
the horizontal hair, by two vertical screws, g and h. 

Before using the instrument it must be adjusted , that is, 
the parts must be brought to their proper relative positions : 
there are four principal adjustments. 

First adjustment.— To fix the intersection of the spider's 
lines in the line of collimation or axis of the telescope. 

Having screwed the tripod to the instrument, extend 
the legs, and place them firmly. Then loosen the clamp- 
screw S of the vernier plate, and direct the telescope to a 
small, well-defined, and distant object. By means of a 
small pin on the under side of the telescope, slide the 
eye-glass till the spider’s lines are seen distinctly; then with 
the thumb-serev/ X, which forces out and draws in, the 
object-glass, adjust this glass to its proper focus, when the 
object, as well as the spider’s lines, will be distinctly seen: 
after which, by the tangent-screw T and the thumb-screw 
iv, bring the intersection of the spider’s lines exactly upon 
a well-defined point of the object. 

Having done this, revolve the telescope in the Y : s half 
round, when the v attached level mn, will come to the upper 
side. See, in this position, if the horizontal hair appears 
above or below the point, and in either case, loosen one, 
and tighten the other, of the two screws that work the 
horizontal hair, till the horizontal hair has been carried 
over half the space between its last position and the ob¬ 
served point. Carry the telescope back to its place; di¬ 
rect again the intersection of the spider’s lines to the point, 
and repeat the operation till the horizontal hair neither 
ascends nor descends, while the telescope is revolved. A 
similar process will arrange the vertical hair, and the line 
of collimation is then adjusted. 

Second adjustment. —To make the axis of the attached 
level of the upper telescope , parallel to the line of collimation. 

Turn the vernier plate, till the telescope c^nes directly 


SEC. I] 


OF THE THEODOLITE. 


73 


over two of the levelling screws, between the plates BE 
and FG. Turn these screws contrary ways, keeping them 
firm against the plate FG , till the bubble of the level mn, 
stands at the middle of the tube. Then, open the loops, 
and reverse the telescope. If the bubble still stands in the 
middle of the tube, the axis of the tube is horizontal; but 
if not, it is inclined, the bubble being at the elevated end. 
In that case, by means of the small vertical screws m and 
n, at the ends of the level, raise the depressed end, or de¬ 
press the elevated one, half the inclination; and then, with 
the levelling screws, bring the level ifito a horizontal posi¬ 
tion. Reverse the telescope in the Y’s, and make the 
same correction again; and so on, until the bubble stands 
in the middle of the tube, in both positions of the tele¬ 
scope : the axis of the level is then horizontal. Let the 
telescope be now revolved in the Y's< If the bubble con¬ 
tinue in the middle of the tube, the axis of the level is 
not only horizontal, but also parallel to the line of colli- 
mation. If, however, the bubble recede from its centre, 
the axis of the level is inclined to the line of collimation, 
and must be made parallel to it by means of two small 
antagonistic screws, (one of which is seen at p,) which work 
horizontally. By loosening one of them, and tightening 
the other, the level is soon brought parallel to the line of 
collimation, and then, if the telescope be revolved in the 
Y’s, the bubble will continue in the middle of the tube. 

It is difficult to make the first part of this adjustment, 
while the axis of the level is considerably inclined to the 
line of collimation; for, if the level were truly horizontal 
in one position of the telescope, when the telescope is re¬ 
versed, the bubble would not stand in the middle of the 
tube, except in one position of the level. This suggests 
the necessity of making the first part of the adjustment 
with tolerable accuracy; then, having made the second 
with care, let the first be examined, and proceed thus till 
the adjustment is completed. 

Third adjustment.— To make the axes of the levels on 
the limb perpendicular to the axis of the instrument. 

This adjustment is effected, partly by the levelling 


74 


ELEMENTS OF SURVEYING. [BOOK II 


screws, and partly by the thumb-screw Z. Turn the ver¬ 
nier plate, until the upper telescope comes directly over 
two of the levelling screws, then turn them contrary ways, 
till the upper telescope is horizontal; after which, turn the 
vernier plate 180°, and if the bubble of the level remains 
in the middle of the tube, one line of the limb is horizon 
tal. But if the bubble recede from the centre of the level, 
raise the lower, or depress the upper end, one-half by the 
levelling screws, the other by the thumb-screw Z , till it is 
brought into a horizontal position. Turn the vernier plate 
again 180°, and if the level be not then horizontal, make 
it so, by dividing the error as before, and repeat the op¬ 
eration until the line of the limb is truly horizontal. 
Then turn the vernier plate 90°, and level as before. 
The limb ought now to be truly horizontal; but lest the 
first horizontal line may have been changed, in obtaining 
the second, it is well to bring the telescope and level two 
or three times over the levelling screws, until an entire 
revolution can be made without displacing the bubble from 
the middle of the tube. As this can only be the case 
when the level revolves around a vertical line, it follows 
that the limb will then be-horizontal, and the axis of the 
instrument vertical. Then, by means of the small screws at 
the ends of the levels, bring the bubbles to the centres, and 
the axes of the levels will then be perpendicular to the axis 
of the instrument. 

Fourth adjustment. —To make the axis of the vertical 
limb perpendicular to the axis of the instrument. 

Bring the intersection of the spider's lines of the upper 
telescope upon a plumb line, or any well-defined vertical 
object, and move the telescope with the thumb-screw Z: 
if the intersection of the spider’s lines continue on the ver¬ 
tical line, the axis is horizontal. 

Or,, the adjustment may be effected thus: Direct the 
intersection of the spider’s lines to a well-defined point 
that is considerably elevated: then turn the vertical limb, 
until the axis of the telescope rests on some other well-de¬ 
fined point, upon or near the ground: reverse the tele¬ 
scope, and turn the vernier plate 180°; now, if in elevating 
and depressing the telescope, the line of collimation passes 


SEC. I.] 


VERNIERS. 


75 


\ 


through the two points before noted, the axis is horizontal. 
If it be found, by either of the ,above methods, that the 
axis is not horizontal, it must be made so by the screws 
which fasten the frame-work to the vernier plate. 

There are two important lines of the theodolite, the po¬ 
sitions of which are determined with great care by the 
maker, and fixed permanently. First, the axis of the in¬ 
strument is placed exactly at right angles with the limb 
and vernier plate; and unless it have this position] the 
vernier plate will not revolve at right angles to the axis, 
as explained in the third adjustment. Secondly, the line 
of collimation of the upper telescope is fixed at right angles 
to the horizontal axis of the vertical limb. We can as¬ 
certain whether these last lines are truly at right angles, 
by directing the intersection of the spider’s lines to a well- 
defined point; then removing the caps which confine the 
horizontal axis in its supports, and reversing the axis: if 
the intersection of the spider’s lines can be made to cover 
exactly the same point, without moving the vernier plate, 
the line of collimation is at right angles to the axis. 

If the theodolite be so constructed that either of the 
Y's admits of being moved laterally, so as to vary the 
angle between the horizontal axis and the line of collima¬ 
tion, these lines may be adjusted at right angles to each 
other, if they have not been so placed by the maker. 

The lower telescope being used merely as a guard, re¬ 
quires no adjustment, although it is better to make the 
axis, about which its vertical motions are performed, hori¬ 
zontal, or perpendicular to the axis of the instrument; and 
this is easily effected by means of the two small screws k 
and Z, which work into the slide A', that 'is connected with 
the horizontal axis. 

Having explained the methods of properly adjusting the 
theodolite, we will now explain the particular uses of its 
several parts, and the manner of measuring angles. 


VERNIERS. 

21. Before explaining the vernier, as applied to the tne- 
odolite, we shall discuss the general theory of verniers. 


76 


ELEMENTS OF SURVEYING. [ROOK IL 


A Yernier is a contrivance for measuring parts of the 
equal spaces marked off on a given scale or limb. 

It is a graduated scale, so arranged, as to cover an ex¬ 
act number of equal spaces on the primary scale or limb , 
to which it is applied. It is divided into a number of 
equal parts, greater by one than the number of equal spaces 
which it covers on the limb. 

The vernier may be applied to any scale of -equal parts. 
The modes of its application are extremely various; the 
principle, however, is the same in all, and may be illus¬ 
trated by a simple diagram. 


8 9 JO 1J 12 13 It Jo 16 _ 17 18 19 














c 





I 

B 


0 J H 3 4 0 6 7 8 9 10 


Let AB be any limb or scale of equal parts, one of 
which let us suppose equal to b. Let CD be a vernier, 
equal in length to nine of these parts, and itself divided 
into ten equal spaces, each one of which is then equal to 
nine-tenths of b. The difference between a spacq on the 
limb'and a space on the vernier, is therefore equal to one- 
tenth of b or j-<jb. This is the least space that can be meas¬ 
ured by means of the vernier, and is called the least count; 
hence, 

The least count of a vernier is equal to one of the equal 
divisions of the limb divided by the number of spaces on the 
vernier. < 

22. The true reading of the instrument, for any position 
of the vernier, expresses the distance from the point where 
the graduation on the limb begins, marked 0, to the 0 
point of the vernier. In the diagram, that distance is ex¬ 
pressed by nine units of the scale, or 9. 

If, now, the vernier be moved till the division 1 coin¬ 
cides with the division 10 of the limb, the 0 point will 
have advanced along the limb a distance equal to j\b, 
and the reading will become 9 + If we again 

move the vernier till the division 2 coincides with the di¬ 
vision 11 of the scale, the 0 point will have advanced an 
additional distance, equal to b , and the reading becomes 


























SEC. I.] MEASUREMENT OF ANGLES. 77 

9 + t 2 o l ') ; Tv-hen 3 coincides with division 12, the reading 
will become 9 + and so on, till finally, when the point 

10 coincides with 19 of the scale, the distance 9 will have 
been increased by \ 9 G b, and will become 10, as it should, 
since, in that case, the 0 point will have been moved a whole 
space, and will coincide with the division 10 of the limb. 
Hence, the following rule for reading an instrument which 
has a vernier. 

Read the limb in the direction of the graduation up to the 
division line next preceding the 0 point of the vernier ; this 
is called the reading on the limb. Look along the vernier till 
a dividing line is found to coincide with a line of the limb: 
multiply the number of this first line by the least count of the ver¬ 
nier : this is the reading on the vernier: the sum of these two 
readings is the reading of the instrument. 

23. In the theodolite described, the limb is divided into 
half degrees, and 30 spaces on the vernier cover 29 spaces 
on the limb. Hence, the least count of this instrument is 

of a half degree or 1'. Fig. 2, Plate 1, exhibits the 
vernier of the horizontal limb, and Fig. 3 the vernier of 
the vertical limb. 

TO MEASURE A HORIZONTAL ANGLE WITH THE THEODOLITE. 

24. Place the axis of the instrument directly over the 
point at'which the angle is to be measured. This is ef¬ 
fected by means of a plumb, suspended from the plate 
which forms the upper end of the tripod. 

Having made the limb truly level, place the 0 of the 
vernier at 0 or 360° of the limb, and fasten the clamp- 
screw jS of the vernier plate. Then, facing in the direc¬ 
tion between the lines which subtend the angle to be mea¬ 
sured, turn the limb with the outer spindle, until the tele¬ 
scope points to the object on the left, very nearly. Clamp 
the limb with the clamp-screw ii, and by means of the 
tangent screws L and Z\ bring the intersection of the 
spider’s lines to coincide exactly with the object. 

Having loosened the clamp-screw Q of the lower tele¬ 
scope MN, direct it with the thumb-screw P to the 


78 


ELEMENTS OF SURVEYING. [BOOK II 


same object at which the upper telescope is directed; then 
tighten the clamp-screw Q. This being done, loosen the 
clamp-screw S of the vernier plate, and direct the telescope 
to the other object: the arc passed over by the 0 point 
of the vernier, is the measure of the angle sought. 

The lower telescope having been made fast to the limb, 
will indicate any change of the position of the limb, should m 
any have taken place; and, as the accuracy of the mea¬ 
surements depends on the fixedness of the limb, the lower 
telescope ought to be often examined, and if its position has 
been altered, the limb must be brought back to its place by 
the tangent-screw L. 

It is not necessary to place the 0 point of the vernier 
at the 0 point of the limb, previously to commencing the 
measurement of the angle, but convenient merely; for, 
whatever be the position of this point on the limb, it is 
evident that the arc which it passes over is the true mea¬ 
sure of the horizontal angle. If, therefore, its place be 
carefully noted for the first direction, and also for the sec¬ 
ond, the difference of these two readings will be the true 
angle, unless the 0 point of the vernier shall have passed 
the 0 point of the limb, in which case the greater reading 
must be subtracted from 860°, and the remainder added to 
the less. 

TO MEASURE A VERTICAL ANGLE. 

25. We shall first explain the method of determining 
the index error. Having levelled the horizontal limb, di¬ 
rect the telescope to some distinctly marked object as the 
top of a chimney, and read the instrument. Reverse the 
telescope in the Y's, and turn the vernier plate 180°, and 
having directed the telescope to the same object, again 
read the instrument. If the two readings are the same, 
the limb is adjusted; that is, the 0 of the limb coincides 
with the 0 of its vernier, when the axis of the telescope 
is parallel to the horizontal limb. 

When the reading found with the eye end of the tele¬ 
scope nearest the vernier, is greater than that obtained in 
the reversed position, the true elevation of the object 


SEC. I.] 


PRACTICAL PROBLEMS. 


79 


which is equal to a mean of the readings, may be obtained 
by subtracting half their difference from the first reading. 
If the first reading is less than the second, the half differ¬ 
ence must be added to the first. Hence, 

To find the index error , take the reading of the limb when 
the telescope is directed to a fixed object, first with the eye end 
of the telescope nearest the vernier , and then with the telescope 
and vernier plate both reversed. Take half the difference of 
these readings , and affect it with a minus sign if the first is 
greater, or a plus sign if the second is the greater; this is equal 
to the index error. 

Let the operation be repeated several times, using dif¬ 
ferent objects, and a mean of the errors will be more cor¬ 
rect than the result of a single observation. 

26. Having determined the index error, let the axis of 
the telescope be directed to any point either above or be¬ 
low the plane of the limb, and read the arc indicated by 
the 0 of the vernier. To the arc so read apply the proper 
correction, if any, and the result will be the true angle of 
elevation or depression. 

The angle of elevation may be more correctly found by 
taking the elevation of the object, and repeating the obser¬ 
vation with the telescope and vernier plate reversed, and 
then taking a mean of the readings for the angle required. 

MEASUREMENTS WITH THE TAPE OR CHAIN ONLY. 

27. It often happens that instruments for the measur- 
ment of angles cannot be easily obtained; we must then 
rely entirely on the tape or chain. 

We now propose to explain the best methods of deter¬ 
mining distances, without the aid of instruments for the 
measurement of horizontal or vertical angles. 

1. To trace , on the ground , the direction of a right line , that 

shall be perpendicular at a given point , to a given right 

line. 

FIRST METHOD. 

28. Let BO be the given right line, and A the given 


80 


ELEMENTS OF SURVEYING. [BOOK IL 


point. Measure from A, on the 
line BG, two equal distances AB, 

AC\ one on each side of the point 
A. Take a portion of the chain 
or tape, greater than AB, and 
place one extremity at B, and with the other trace the arc 
of a circle on the ground. Then remove the end which 
was at B, to C, and trace a second arc intersecting the 
former at I). The straight line drawn through B and A 
will be perpendicular to BC at A. 


D- 

* 


a. 


c 


SECOND METHOD. 


29. Having made AB = AC, take D 

any portion of the tape or chain 
considerably greater than the dis¬ 
tance between B and 0. Mark 
the middle point of it, and fasten 
its two extremities, the one at B 
and the other at 0. Then, taking the chain by the middle 
point, stretch it tightly on either side of BO, and place a 
staff at D or E: DAE will be the perpendicular re¬ 
quired. 



THIRD METHOD. 


SO. Let AB be the given line, 
and C the point at which the per¬ 
pendicular is to be drawn. From 
the point C measure a distance CA 
equal to 8. With C as a centre, 
and a radius equal to 6, describe 
an arc on either side of AB : then, 


A- 


f 

A 


C 


‘it 


GB 


with 1 as a centre, and a radius equal to 10, describe a 
second arc intersecting at E, the one before described: 
then draw the line EG, and it will be perpendicular to 
AB at G. 


Remark. Any three lines, having the ratio of 6, 8, and 
10, form a right-angled triangle, of which the side corre¬ 
sponding to 10 is the liypotlienuse. 








SEC. I] 


SURVEYING CROSS. 


81 


FOURTH METHOD. 

31. Let AD be the given right 
line, and D the point at which 
the perpendicular is to be drawn. 

Take any distance on the tape * 
or chain, and place one extrern- ^ 
ity at D , and fasten the other 
at some point, as E , between 
the two lines which are to form the right angle. Place a 
staff at E. Then, having stationed a person at D , remove 
that extremity of the chain and carry it rouncl until it 
ranges on the line DA at A. Place a staff at A : then 
remove the end of the chain at, i, and carry it round 
until it falls on the line AE at F. Then place a staff at 
F; ADF will be a right angle, being an angle in a 
semicircle. 

32. There is a very simple instrument, used exclusively 
in laying off right angles on the ground, which is called 
the 

SURVEYING CROSS. 

PL 2, Fig. 1. This instrument consists of two bars, AB 
and CD, permanently fixed at right angles to each other, 
and firmly attached at E to a pointed staff, which serves 
as a support. Four sights are screwed firmly-to the bars, 
b y means of the screws a, b, c, and d. 

As the only use of this instrument is to lay off right 
angles, it is of the first importance that the lines of sight 
be truly at right angles. To ascertain if they are so, let 
the bar AB be turned until its sights mark some distinct 
object; then look through the other sights, and place a 
staff on the line which they indicate: let the cross be then 
turned until the sights of the bar AB come to the same 
line: if the other sights are directed to the first object, the 
lines of sight are exactly at right angles. 

The sights being at right angles, if one of them be 
turned in the direction of a given line, the other will mark 
the direction of a line perpendicular to it, at the point 
where the instrument is placed. 





82 


ELEMENTS OF SURVEYING. [BOOK IL 


II. From a given point without a straight line, to let fall a 

perpendicular on the line. 

83. Let C be the given point, and AB the given line. 
From G measure a line, as 
CA, to any point of the line AB. 

From A , measure on AB any 
distance as AF, and at F erect 
FE perpendicular to AB. T' £> 

Having stationed a person at A, measure along tire per¬ 
pendicular FE until the forward staff is aligned on the line 
AC: then measure the distance AE. How, by similar tri¬ 
angles, we have, 

AE : AF : : AC : AD, 

in which all the terms are known except AD, which may, 
therefore, be found. The distance AD being laid off from 
A , the point D, at which the perpendicular CD meets AB, 
becomes known. If we wish the length of the perpen¬ 
dicular, we use the proportion, 

AE : EF : : AC : CD, 

in which all the terms are known, excepting CD: there¬ 
fore, CD may be determined. 



IIL To determine the horizontal distance from a given point to 

an inaccessible object. 

FIRST METHOD. 

34. Let A be an inaccessible object, and E the point 
from which the distance is to be measured. 

At E lay off the right angle 
AED, and measure in the di¬ 
rection ED, any convenient dis¬ 
tance to D, and place a staff 
at D. Then measure from E, 
directly towards the object A, 
a distance EB of a convenient 
length, and at B lay off a line JD 



l 


F 


B 


E 


BC perpendicular to EA. Measure along the line BC, 









% 


SEC. I] PRACTICAL PROBLEMS. 83 

until a person at D shall range the forward staff on the 
line DA. Now, DF is known, being equal to the differ¬ 
ence between the two measured lines DE and OB. Hence, 

similar triangles, 

DF : FO :: DE : EA, 

m which proportion all the terms are known, except th 
fourth, which may, therefore, be found. 

SECOND M 

35. At the point E lay off 
EB perpendicular to the line 
EA, and measure along it any 
convenient distance, as EB. 

At B lay off the right an¬ 
gle EBD , and measure any dis¬ 
tance in the direction BD. Let 
a person at D align a staff on 
DA, while a second person at B aligns it on BE: the 
staff will thus be fixed at 0. Then measure the dis¬ 
tance BO. 

The two triangles BCD and CAE being similar, we 
have, 

BC : BD : : CE : EA, 

m which all the terms are known, except the fourth, which 
may, therefore, be found. 

THIRD METHOD. 

0 

36. Let B be the given point, and A the inaccessible 
object; it is required to find BA. 

Measure any horizontal base 
line, as BC. Then, having 
placed staves at B and C, 
measure any convenient dis¬ 
tances BD and CE, such that 
the points D, B, and A, shall 
be in the same right line, as 
also, the points E, C, and A; 
then measure the diagonal lines 
DC and EB. 



1THOD. 

























ELEMENTS OF SURVEYING. [BOOK IL 


84 


Now, in the triangle BEG\ 
the three sides are known, 
therefore, the angle ECB can 
be found. In the triangle CDB, 
the three sides are also known, 
therefore the angle CBD can be 
determined. These angles be¬ 
ing respectively subtracted from 
180°, the two angles ACB and 
ABC become known; and hence, 
in the triangle ABO\ we have two 
side, to find the side BA. 



angles and the included 


IY. To find the altitude of an object, ivhen the distance to the 
vertical line passing through the top of it is known. 

87. Let CD be the altitude required, and A C the known 
distance. 

From A, measure on 
the line AC, any con¬ 
venient distance AB, and 
place a staff vertically 
at B. Then placing the 
eye at A, sight to the 
object D, and let the 
point, at which the line AD cuts the staff BE, be marked. 
Measure the distance BE on the staff; then, 



AB : BE : 

whence CD becomes known. 


AC 


CD, 


If the line AC cannot be measured, on account of in¬ 
tervening objects, it may be determined by calculation, as 
in the last problem, and then, having found the horizontal 
distance, the vertical line is readily determined, as before. 




















SEC. II] 


AREA OF LAND. 


85 


SECTION II. 

AREA OR CONTENTS OF GROUND.—LAYING OUT LAND. 

1. We come next to the determination of the area or 
superficial contents of ground. 

The surface of the ground being, in general, broken 
and uneven, it is impossible, without great trouble and ex¬ 
pense, to ascertain its exact area or contents. To avoid 
this inconvenience, it has been agreed to refer every sur¬ 
face to a horizontal plane: that is, to regard all its bound¬ 
ing lines as horizontal, and its area as measured by that 
portion of the horizontal plane which the boundary lines 
enclose. 

For example, if A BCD were a 
piece of ground having an uneven 
surface, we should refer the whole 
to a horizontal plane, and take 
for the measure of the area that 
part of the plane which is inclu¬ 
ded between the bounding hori¬ 
zontal lines AB , BC\ CD , DA. 

In estimating land in this manner, the sum of the areas 
of all the parts into which a tract may be divided, is equal 
to the area, estimating it as an entire piece: but this would 
not be the case if the areas of the parts had reference to 
the actual surface, and the area of the whole were calcu¬ 
lated from its bounding lines. 

2. The unit of measure of a quantity is a quantity of 
the same kind regarded as a standard, and with which all 
quantities of that kind may be compared. For lines, the 
unit is a right line of a known length, as 1 foot, 1 link, 1 
chain, or any other fixed distance. 

It has been already observed (Bk. II., Sec. I., Art. 16), 
that Gunter’s chain of four rods or 66 feet in length, and 
which is divided into 100 links, is the chain in general 







86 


ELEMENTS OF SURVEYING. [BOOK II 


use among surveyors. In measuring land, the length of 
this chain is generally taken for the unit of linear measure. 


3. The unit of measure for surfaces is a square de¬ 
scribed on the unit of linear measure. 


1 foot. 


Thus, 1 square foot, 


1 square yard or 9 square feet, 


1 yard = 3 feet. 


1 square chain, or 16 square rods. 


1 chain = 4 rods. 



When, therefore, the linear measures of ground are feet, 
yards, rods, or chains, the superficial measures are square 
feet, square yards, square rods, or square chains; and the 
numerical expression for the area is the number of times 
which the unit of superficial measure is contained in the 
land measured. 


4. An acre is a surface equivalent in extent to 10 square 
chains; that is, equivalent to a rectangle of which one side 
is ten chains, and the other side one chain. 

One quarter of an acre is called a rood. 

Since the chain is 4 rods in length, 1 square chain con¬ 
tains 16 square rods; and therefore, an acre, which is 10 
square chains, contains 160 square rods, and a rood con¬ 
tains 40 square rods. The square rods are called perches. 

5. Land is generally computed in acres, roods, and 
perches, which are respectively designated by the letters 

A. R. P. 

























SEC. II] 


AREA OF LAND. 


87 


When the linear dimensions of a survey are chains or 
links, the area will be expressed in square chains or square 
links, and it is necessary to form a rule for reducing this 
area to acres, roods, and perches. For this purpose, let us 
form the following 


TABLE. 


Miles. 

Acres. 

Roods. 

Sq. Chains. 

Perches. 

Sq. Links. 

1 

640 

1 

2560 

4 

1 

6400.0 

10.0 

2.5 

1.0 

102,400 

160 

40 

16 

1 

64,000,000 

100,000 

25,000 

10,000 

625 


1 square mile = 6400 square chains = 640 acres. 


Now, when the linear dimensions are links, the area 
will be expressed in square links, and may be reduced to 
acres by dividing by 100000, the number of square links 
in an acre: that is, by pointing off five decimal places 
from the right hand. 

If the decimal part be then multiplied by 4, and five 
places of decimals pointed off from the right hand, the 
figures to the left will express the roods. 

If the decimal part of this result be now multiplied by 
40, and five places for decimals pointed off, as before, the 
figures to the left will express the perches. 

If one of the dimensions be in links, and the other in 
chains, the chains may be reduced to links by annexing 
two ciphers : or, the multiplication may be made without 
annexing the ciphers, and the product reduced to acres and 
decimals of an acre, by pointing off three decimal places 
from the right hand. 

When both the dimensions are in chains, the product 
is reduced to acres by dividing by 10, or pointing off one 
decimal place. 

From which we conclude; that, 

1st. If linJcs be multiplied by links, the product is reduced to 
acres by pointing off five decimal places from the right hand . 















88 


ELEMENTS OF SURVEYING. [BOOK IL 


2d. If chains he multiplied hy links , the product is reduced 
to acres hy pointing off three decimal places from the right hand . 

3d. If chains he multiplied hy chains , the product is reduced 
to acres hy pointing off one decimal place from the right hand. 

6. Since there are 16.5 feet in a rod, a square rod is 

equal to . 16.5 X 16.5 = 272.25 square feet. 

If the last number be multiplied by 160, we shall have, 

272.25 X 160 = 43560 = the square feet in an acre. 

Since there are 9 square feet in a square yard, if the 
last number be divided by 9, we obtain, 

4840 = the number of square yards in an acre. 

PROBLEM i. 

7. To find the area of a piece of ground in the form 
of a square, rectangle, or parallelogram. 

Multiply the base hy the altitude , and the product will express 
the area (Geom., Bk. IV., Prop. IV. and V.) 

1. To find the area of the rectangular d c 

field ABCD. 

Measure the two sides AB , BO : let us 
suppose that we have found AB — 14 chains 
27 links, and BG— 9 chains 75 links. Then, A B 

Mi? =1427 links, 

BC — 975 links, 

AB X BO= 1391325 square links, 

= 13.91325 acres. 

4 

3.65800 roods, 

40 

26.12000 perches. 

' Ans. 13 A. 8 R. 26P. 

2. What is the area of a square field, of which the 
sides are each 33 ch. 81.? 


Ans. 109 A. IB. 29 P. 







SEC. II.] 


AREA OF LAND. 


89 


3. What are the contents of a rectangular held, of which 
the longer side is 49 ch. 27 L, and the shorter 38 ch. 7 1.? 

Ans. 187-4. 2P. IIP. 

4. What are the contents of a held in the form of a 
parallelogram, of which the base is 35 ch. 65 1., and alti¬ 
tude 51 ch. 41.? 

Ans. 1814.. 3P. 33P. 


PROBLEM II. 

8. To hnd the contents of a piece of land in the form 
of a triangle. 


FIRST METHOD. 



Measure either side of the triangle 
as BC\ and from the opposite angle 
A let fall a perpendicular AD, and 
measure this perpendicular; then , mid- 
tiply the base and perpendicular to¬ 
gether, and divide the product by 2, 
the result will express the area of the triangle. Or , the area 

is equal to the base multiplied by half the perpendicular , or to 
the perpendicular multiplied by half the base (Gegm., Bk. IV., 
Prop. VI.). 

1. What are the contents of a triangle whose base is 
25 ch. 1 1., and perpendicular 18 ch. 14 1. ? 

Ans. 224. 2 R. 29P. 

2. What are the contents of a triangle whose base is 
15.48 chains, and altitude 9.67 chains ? 

Ans. 74. IP. 38P. 


SECOND METHOD. 

Measure two sides and their included angle. Then , add 
together the logarithms of the two sides and the logarithmic sine 
of their included angle; from this sum subtract the logarithm 
of the radius , which is 10, and the remainder will be the loga¬ 
rithm of double the area of the triangle. Find , from the table , 




90 


ELEMENTS OF SURVEYING. [BOOK II 


the number answering to this logarithm, and divide it by 2 / the 
quotient ivill be the required area (Geom. Mens., Art. 6). 

1. In a triangle ABO, suppose that we have found 
AB= 57.65 eh., A(7= 125.81 ch., and the included angle 
CAB =57° 25': required the area. 

Let the required area "be designated by Q; then, 

-Hog AB 57.65 . . . 1.760799 
+ log AC 125.81 . . 2.099715 

+ log sin A 57° 25' . 9.925626 

— log B .10 

= 6111.4 .... 3.786140. 

= 3055.7 square chains. 

Ans. 305A. 2 R. IIP. 

Kemark. In this example, the links are treated as de¬ 
cimal parts of the chain; the result, therefore, is ^n square 
chains and decimal parts of a square chain. 

2. What is the area of a triangle whose sides are 30 
and 40 chains, and their included angle 28° 57' ? 

Ans. 29A. OR. 7 P. 


log 2 Q = 
2 Q 

And Q 


third method. 

Measure the three sides of the triangle. Then, add them 
together and take half their sum. From this half sum subtract 
each side separately. Then, multiply the half sum and the 
three remainders together , and extract the square root of the pro¬ 
duct: the result ivill be the area (Geom. Mens., Art. 7). 

Or, after having obtained the three remainders, add together 
the logarithm of the half sum and the logarithms of the re¬ 
spective remainders, and divide their sum by 2; the quotient 
will be the logarithm of the area. 

1. Find the area of a triangular piece of ground whose 
sides are 20, 30, and 40 chains. 






SEC. II.] 


AREA OF LAND. 


91 


BY FIRST RULE. 

20 45 45 45 

30 -20 - 30 - 40 

40 . 25 1st rem. 15 2d rem. ~5 3d rem. 

2)90 — — _ 

45 = half sum. Then, 

45 X 25 X 15 X 5 = 84375 : and V84375 = 290.4737 = the 
area. 

Ans. 29 A. OB. 8P. 

2. What is the area of a triangle whose sides are 2569, 
4900, and 5035 links? 


BY SECOND RULE. 

2569 6252 6252 6252 

4900 -2569 -4900 -5035 

5035 3683 1st rem. 1352 2d rem. 1217 3d rem. 

2 )12504 ‘ 

6252 = half sum. 


Then, 


log 6252 
log 3683 
log 1352 
log 1217 


Area in square h'nks, 6155225 


. . . 3.796019 
. . . 3.566202 
. . . . 3*130977 
. . . 3.085291 
2)13.578489 
. . . . 6.789244. 

Ans. 61 A. 2 B. 8P. 


PROBLEM III. 

9. To find the area of a piece of land in the form of 
a trapezoid. 

Measure the two parallel sides , and also the perpendicular 
distance between them. Add the two parallel sides together , 
and take half the sum,; then multiply the half sum by the 
perpendicular, and the product will be the areaj (Geom., Bk. 
IV., Prop. VII.) 






















92 


ELEMENTS OF SURVEYING. [BOOK II 


1. What is the area of a trapezoid, 
of which the parallel sides are 30 and 
49 chains, and the perpendicular distance 
between them 16 cli. 60 L, or 16.60 chains ? 

30 + 49 = 79; dividing by 2, gives . . '39.5 
multiply by.16.60 

area in square chains. 655.700. 

Ans. 65+. 2 B. 11 P. 



2. Required the contents, when the parallel sides are 20 
and 32 ch., and the perpendicular .distance between them 
26 ch. 

Ans. 67A. 2 B. 16P 


PROBLEM IV. 


10. To find the area of a piece of land in the form of 
a quadrilateral. 

Measure the four sides of the quadrilateral , and also one of 
the diagonals: the quadrilatercd will thus he divided into two 
ti'iangles, in both of ivhich cdl the sides ivill he known. Then, 
find the areas of the triangles separately, and their sum will he 
the area of the quadrilcderal. 


1. Suppose that we have measured 
the sides and diagonal AC\ of the 
quadrilateral ARCD , and found 
AB= 40.05 ch. CD — 29.87 ch., 
BC = 26.27 ch. AD = 3 7.07 ch., 
and AC=55 ch.: 


I) 



required the area of the quadrilateral. 

Ans. 101 A. IB. 15 P. 


Remark. Instead of measuring the four sides of the 
quadrilateral, we may let fall the perpendiculars Bh } Dg , on 
the diagonal AC. The area of the triangle may then be 
determined by measuring these perpendiculars and the di¬ 
agonal A C. The perpendiculars are Dg = 18.95 ch., and 
Bh = 17.92 ch. 










SEC. II.] 


AREA OF LAND. 


93 


PROBLEM V. 

11. To find tlie contents of a field having any number 
of sides. 

Measure the sides of the field and also the diagonals: the 
three sides of each of the triangles into which the field will he 
thus divided will then he known , and the areas of the triangles 
may then he calculated hy the preceding rules. Or, measure 
the diagonals , and from the angular points of the field draw 
perpendiculars to the diagonals and measure their lengths: the 
base and perpendicular of each of the triangles will then he 
known. 


1. Let it be required to determine the contents of the 
field ABODE , having five sides. 

Let us suppose that we have mea¬ 
sured the diagonals and perpendicu¬ 
lars, and found. 


A 0=36.21 ch., EC =3 9.11 ch., 

AZ> = 4.08 ch., Dd=7.26 ch., 

Aa = 4.19 ch.; required the area of the field. 



Area of triangle ABO= 73.8684 

square chains, 

area of 

“ CDE= 141.9693 

a 

a 

area of 

“ ACE= 81.7399 

a 

a 

area of 

ABODE = 297.5776 

a 

a 


• 

Ans. 29A. 

3 R. IP. 


PROBLEM VI. 


12. To find the contents of a long and irregular figure, 
bounded on one side by a straight line. 

Suppose the ground, of which the contents are required, 
to be of the form ABEeda , bounded on one side by the 
right line AE , and on the other by the curve edca. 


At A and A, the extremities of 
the right line AE, erect the two per¬ 
pendiculars Aa, Ee, and on each of 
them measure the breadth of the land. 















94 


ELEMENTS OF SURVEYING. [BOOK IL 


Then divide the base into any convenient number of equal 
parts, and measure the breadth of the land at each point 
of division. 

Add together the intermediate breadths and half the sum of 
the two extreme ones: then multiply this sum by one of the 
equal parts of the base line 1 and the product will be the re - 
quired area very nearly (Mens. Art. 11). 

1. The breadths of an irregular figure, at five equidis¬ 
tant places, being 8.20 eh., 7.40 eh., 9.20 eh., 10.20 eh., and 
8.60 chains, and the whole length 40 chains, required the 
area. 

8.20 4)40 

8.60 10 one of the equal parts. 

2 )1^80 “ 

8.40 mean of the extremes, 85.20 sum, 

7.40 _10 

9.20 area 352.00 square ch. 

10.20 

35.20 sum. 

Ans. 35A. 32 P. 

2. The length of an irregular piece of land being 21 ch., 
and the breadths, at six equidistant points, being 4.35 ch., 
5.15 ch., 8.55 ch., 4.12 ch., 5.02 ch., and 6.10 chains: re¬ 
quired the area. 

Ans. 9 A. 2 R. 80P. 

3. The length of an irregular' piece of land is 80 ch., 
and the breadths at nine equidistant points are 5.75 ch., 
6.12 ch., 4.80 ch., 5.09 ch., 3.87 ch., 5.17 ch., 6.00 ch., 
8.94 ch., and 5.95 ch.: what is the area ? 

Ans . 40M. 8P. 14P. 

4. The length of an irregular field is 39 rods, and its 

breadths at five equidistant places are 4.8, 5.2, 4.1, 7.3, and 
7.2 rods: what is its area? Ans. 220.35 sq. rods. 

Eemark. If it is not convenient to erect the perpen¬ 
diculars at equal distances from each other, the areas of 
the trapezoids, into which the whole figure is divided, 
must be computed separately • their sum will be the re* 
quired area. 









SEC. II.] 


AREA OF LAND. 


95 


PROBLEM VII. 


13. To find the area of a piece of ground in the form 
of a circle. 


Measure the radius AC: then multiply 
the square of the radius by 3.1416 (Mens., 
Art. 15.). 



1. To find the area of a circular piece of land, of which 
the diameter is 25 ch. 


Ans. 49 A. OR. 14P. 


PROBLEM VIII. 

14. To find the contents of a piece of ground in the 
form of an ellipse. 

c 

Measure the semi-axes AE\ CE. Then 
multiply them together , and their product 

by 3.1416. 

D 

1. To find the area of an elliptical piece of ground, of 
which the transverse axis is 16.08 ch., and the conjugate 
axis 9.72 ch. 

Ans. 12 A. 1 R. 4P. 

Remark I. The following is the manner of tracing an 
ellipse on the ground, when the two axes are known. 

From (7, one of the extremities of the conjugate axis 
as a centre, and AE half the transverse axis as a radius, 
describe the arc of a circle cutting AE in the two" points 
F and G : these points are called the foci of the ellipse. 

Then, take a tape, the length of which is equal to MP, 
and fasten the two ends, one at the focus F, the other at 
the focus G. Place a pin against the tape and move it 
around, keeping the tape tightly stretched: the extremity 
of the pin will trace the curve of the ellipse. 

Remark II. In determining the contents of ground, in 
the examples which have been given, the linear dimensions 
have been taken in chains and decimals of a chain. 








96 


ELEMENTS OF SURVEYING. [BOOK IL 


If tlie linear dimensions were taken in terms of any 
other unit, they may be readily reduced to chains. I or, 
a chain is equal to 4 rods, equal to 22 yards, equal to 66 
feet. Hence, 

1st. Rods may be reduced to chains and the decimal of a 
chain , by dividing by 4. 

2d. Yards may be reduced to chains and the decimal of a 
chain , by dividing by 22. 

3d. Feet may be reduced to chains and the decimal of a 
chain , by dividing by 66. 

Remark III. If it is thought best to calculate the area, 
without reducing the linear dimensions to chains, the re¬ 
sult can be reduced to acres: 

1st. By dividing it by 160 when it is in square rods 
(Art. 5). 

2d. By dividing it by 4840 when it is in square yards 
(Art. 6). 

3d. By dividing it by 43560 when it is in square feet 
(Art. 6). 



OF LAYING OUT LAND. 


15. The surveyor is often required to lay off a given 
quantity of land, in such a way that its bounding lines 
shall form a particular figure, viz., a square, a rectangle, a 
triangle, &c. He is also often called upon to divide given 
pieces pf land into parts containing given areas, or bearing 
certain relations to each other. 

The manner of making such divisions must always de¬ 
pend on a judicious application of the principles of geom¬ 
etry to the particular case. 

If, for example, it were required to lay out an acre of 
ground in a square form, it would first be necessary to 
find, by calculation, the side of such a square, and then to 
trace, on the ground, a figure bounded by four equal lines 
at right angles to each other. 


SEC. II] 


97 


LAYING OUT LAND. 

PROBLEM I. 

16. To lay out a given quantity of land in a square 
form. 

Reduce the given area to square chains , or square rods: 
then extract the square root , and the result will he the side of 
the required square. This square being described on the ground , 
will be the figure required. 

1. To trace a square which shall contain 15 A. OR. 12 P. 

First, 15A = 00 R = 2400P 

Add, 12P; hence, 

lb A OR 12P=2412P; the square root 

of which is 49.11. 

Therefore, if a square be traced on the ground, of which 
the side is 49.11 rods, it will be the required figure. 

2. To trace a square which shall contain 176A. IP. 24P. 

First, 176A = 1760 square chains, 

1 R= 2.5 “ 

hence, 24P= 1.5 “ 

176A IP 24P=1764 square chains: the square 

root of which is 42. Hence, if a square be traced on the 
ground, of which the side is 42 ch., it will be the required 
figure. 


PROBLEM II. 


17. To lay out a given quantity of land in a rectangu¬ 
lar form, having one of the sides of the rectangle given. 


Divide the given area, reduced to square chains or square 
rods , by the given side of the required rectangle , and the quotient 
will be the other side. Then , trace the rectangle on the ground. 

1. To lay off 240 acres in a rectangular form, one of 
the sides being given, and equal to 80 rods. 

First, 240A = 2400 square chains = 88400 square rods. 

Then, 80)38400(480 rods; which is the required side 
of the rectangle. 


18. A great number of similar problems might be pro¬ 
posed. The solution of them does not, however, properly 
belong to surveying. The laying out of the ground, an^ 

7 * 



98 


ELEMENTS OF SURVEYING. [BOOK II 


the tracing of lines, after the figure and area have been 
determined, are the only parts which appertain to a prac¬ 
tical treatise. The manner of tracing lines having been al¬ 
ready explained, it seems unnecessary to add the numerous 
examples often given under this head of the subject. 


SECTION III. 

SURVEYING WITH THE COMPASS.—DIVIDING LAND. 

1. Before considering the principles involved in the 
method of surveying now to be explained, it will be ne¬ 
cessary to describe the instrument principally used in the 
held, and which is called 


THE CIRCUMFERENTER, OR SURVEYOR’S COMPASS. 

PL 2, Fig. 2. This instrument consists of a compass-box 
DCF , a magnetic needle, a brass plate AB, from twelve to 
fourteen inches long, two plain sights, AF and BG, one 
of which is more fully shown in Fig. 3; and a stand, 
which is sometimes a tripod, and sometimes a single staff 
pointed with iron at the lower end, so that it may be 
placed firmly in the ground. 

The open sights, AF and BG , are placed at right an¬ 
gles to the plate AB , and fastened to it firmly by the 
screws a and b. In each sight there is a large and small 
aperture or slit; the larger aperture being above the smaller 
in one of the sights, and below it in the other. A hair 
or thread of silk is drawn verticallv through the middle 
of the large aperture, as shown in Fig. 3. 

The compass-box DCF is circular, and generally about 
six inches in diameter. At the centre is a small pin, on 
which the magnetic needle is poised. This needle, if al¬ 
lowed to turn freely around the point of support, will settle 
to a state of rest: the direction which it then indicates, is 
that of the magnetic meridian. 



SEC. Ill] 


WITH THE COMPASS. 


99 


In the interior of tlie compass-box, there is a graduated 
circle divided to degrees, and sometimes to half degrees: 
the degrees are numbered from the extremities of the di¬ 
ameter iV/SJ both ways to 90°. 

The length of the magnetic needle is a little less than 
the diameter of the graduated circle, so that the needle can 
move freety around its centre, within the circle, and its 
positions be noted on the graduated arc. 

The compass-box is turned about its centre, without 
moving the plate AB , by means of the milled screw L : 
it is fastened to the plate AB , by the screw P. 

In using the compass, it is important to ascertain the 
exact angle which may be included between the magnetic 
meridian and the direction that may be given to the line 
drawn through the eye and the sights AF and BG. 

To effect this, a small arc HI is described on the bar 
AB, having its centre at the centre of the compass-box. 
This arc is divided to degrees, and sometimes to the parts 
of a degree. A vernier is also used, which is permanently 
attached to the compass-box. 

When the 0 point of this vernier coincides with the 0 
point of the graduated arc III, the line of the compass-box 
marked NS, lies in the plane of the sights. 

Now, supposing the 0 of the vernier to coincide with 
the 0 of the arc HI, if the end of the needle does not 
stand at one of the lines of division of the graduated 
circle, let the whole degrees be read. Then, turn the 
compass-box by means of the screw I, until the needle 
points exactly to the line which marked the whole degrees: 
the space passed over by the 0 of the vernier, shows the 
parts of a degree that are to be added to give the true 
reading. 


SURVEYING WITH THE COMPASS. 

* 

2. The line about which the earth revolves is called its 
axis; and the two points in which the axis meets the sur¬ 
face of the earth, are called the poles. 

3. A plane passed through the axis is called a meridian 




.100 


ELEMENTS OF SURVEYING. 


[BOOK II. 


plane, and its intersection with the surface is called a me¬ 
ridian line or a meridian. 

4. All the meridians converge towards the poles, but 
they vary so little from parallelism within the narrow limits 
of surveys made with the compass, that they may, without 
error, be regarded as parallel straight lines. 

5. If a magnetic needle be suspended freely and allowed 
to settle to a state of rest, a vertical plane passed through 
its axis is called the plane of the magnetic meridian; and its 
intersection with the surface of the earth is called the mag¬ 
netic meridian, or sometimes a North and South line. A 
line perpendicular to a North and South line is called an 
East and West line. 


6. A line traced or measured on the ground, is called 


a course ; and the angle which 
meridian passing through the 
point of beginning, is called 
the hearing. 

^' \ 

Thus, if we start from the 
point A , and measure in the 
direction AB, the line AB is 
the course, and the angle NAB 
is the bearing. 


this line makes with the 


N 



When the course, like AB, falls between the north and 
east points, the bearing is read, north 46° east, and is 
written N. 46° E. 

When the course, like AC, falls between the north and 
west points, the bearing is read, north 30° west, and is 
written N. 30° W. 

When the course, like AF, falls between the south and 
east points, the bearing is read, south 70° east, and is writ¬ 
ten S. 70° E. 


When the course, like AD, falls between the south and 
west points, the bearing is read, south 70° west, and is 
written S. 70° W. 

A course which runs due north, or due south, is desm- 
nated by the letter N or S; and one which runs due east, 
or due west, by the letter E or W. 





SEC. III.] 


WITH THE COMPASS. 


101 


7. If, after having passed over a course, the bearing is 
taken to the back station, this bearing is called the back 
sight , or reverse bearing . 


8. The perpendicular distance between the east and west 
lines drawn through the extremities of a course, is called 
the northing or southing , according as the course is run to¬ 
wards the north or south. This distance is also called the 
difference of latitude , or simply the latitude, because it shows 
the distance which one of the points is north or south of 
the other. 




jj 


E 


Thus, in running the course from A 
to B 1 AC is the difference of latitude, 
north. 

9. The perpendicular distance be¬ 
tween the meridians passing through the 
extremities of a course, is called.the de¬ 
parture of that course, and is east or 
west, according as the course lies on 
the east or west side of the meridian passing through the 
point of beginning. 


c 

II , 

.fT; 

G 

r 

\/f ! 

- ,’F ! 

/ i 

/ 

/* 

A 

. 


s 


Thus, in running the course AB\ CB is the departure, 
east. 


10. It will be found convenient, in explaining the rules 
for surveying with the compass, to attribute to the lati¬ 
tudes and departures the algebraic signs, + and —. 

We shall, therefore, consider every northing as affected 
with the sign +, and every southing as affected with the 
sign —. We shall also consider every easting as affected 
with the sign +, and every westing as affected with the 
sign —. 

11. The meridian distance of a point is its perpendicular 
distance from an assumed meridian. Thus, if the distance 
be estimated from the meridian NS, BC will be the meri¬ 
dian distance of the point B. 


12. The meridian distance of a line is the meridian dis¬ 
tance of its middle point, and is east or west, according as 
this point lies on the east or west side of the assumed me- 







102 


ELEMENTS OF SURVEYING. [BOOK II 


ridian. Thus, FG drawn through the middle point of AB } 
is the meridian distance of the line AB. 

The sign + will always be given to the meridian dis¬ 
tance of a point or line, when it lies on the east of the as¬ 
sumed meridian, and the sign —, when it lies on the west. 

13. When a piece of ground is to be surveyed, we be¬ 
gin at some prominent corner of the field, and go entirely 
around the land, measuring the lengths of the bounding 
lines with the chain, and taking their bearings with the 
compass. It is not material whether the ground be kept 
on the right hand or on the left, and all the rules ‘deduced 
for one of the cases, are equally applicable to the other. 
To preserve uniformity, however, in the language of the 
rules, we shall suppose the land to be always kept on the 
right hand of the surveyor. 


FIELD OPERATIONS. 


14. Let ABCD be a piece of 
ground to be surveyed, A the point 
where the work is to be begun, 

O 7 

and NS a meridian. 

On a sheet of paper, rule three 
columns, as follows, and head them 
stations, bearings, distances. 


Stations. 

Bearings. 

Distances. 

1 

N 31i° W 

10. 

2 

N 62f° E 

9.25 

3 

S 36° E 

7.60 

4 

S 45i° W 

10.40 


Place the compass at A, and take the bearing to B, 
which is FAB: suppose this angle has been found to be 
31i°. The bearing from A to B is then N. 31J° W. En- 





















SEC. III.] 


WITH THE COMPASS. 


103 


ter this bearing in the field notes opposite station 1. 
Then measure the distance from A to B , which we will 
suppose to be 10 ch., and insert that distance opposite sta¬ 
tion 1, in the column of distances. 

We next take the bearing from B to (7, N. 62 J E., and 
then measure the distance BO— 9 ch. 25 1., both of which 
we insert in the notes opposite station 2. 

At station C we take the bearing to D , S. 36° E., and 
then measure the distance CD — 7 ch. 60 L, and place them 
in the notes opposite station 3. 

At D we take the bearing to A, S. 45W., and mea¬ 
sure the distance DA — 10 ch. 40 1. We shall then have 
made all the measurements on the field which are neces¬ 
sary to determine the contents of the ground. 

15. Bemark I. The reverse bearing or back sight, from 
B to A, is the angle ABH\ and since the meridians NS 
and HG are parallel, this angle is equal to the bearing 
NAB. The reverse bearing is, therefore, S. 31|° E. 

The reverse bearing from (7, is S. 62f ° W.; that is, it 
is the angle ICB — GBC. 

And generally, a reverse bearing , or bach sight, is always 
equal to the forward bearing , and differs from it in both of the 
letters by which it is designated. 

16. Bemark II. In taking the bearings with the com¬ 
pass, there are two sources of error. 1st. The inaccuracy 
of the - observations: 2d. Local attractions, or the derange¬ 
ment which the needle experiences when brought into the 
vicinity of iron-ore beds, or any ferruginous substances. 

To guard against these sources of error, the reverse 
bearing should be taken at every station: if this and the ‘ 
forward bearing are of the same value, the work is proba¬ 
bly right; but if they differ considerably, they should both 
be taken again. 

17. Bemark III. If the forward and back sights at the 
end of any course of the survey agree, it may be safely 
assumed, that no local attraction disturbs the needle at 
these points; and hence, that the next foresight is also free 
from such disturbing causes. The error, therefore, from 


104 


ELEMENTS OF SURVEYING. 


[BOOK II. 


local attraction, when it arises, will first show itself in the 
difference between a true foresight and an erroneous back 
sight. 

When this difference appears, subtract the back sight 
from the foresight, and call the difference the correction for 
the next foresight. The correction will be positive when 
the foresight is the larger, and negative when it is less. 

Add this correction, with its proper sign, to the fore¬ 
sight of the next course, when the meridional and longitu¬ 
dinal letters of that course are both the same, or both dif¬ 
ferent from the foresight of the previous course, and sub¬ 
tract it when one of the letters is the same and the other 
different: the result will be the true bearing. The true 
bearing of any other course may be found by the same 
process. 


EXAMPLE. 


True Foresights. 

Back Sights. 

Foresights of next 
Course. 

-— 

Foresights 

Corrected. 

1. S 85° 10' W 

2. N 16° 20'E 

3. N 17° 25' W 

4. S. 47° 18' E 

N 85° 05' E 
S 18° 20' W 
S 16° 10' E 
N 48° 10'W 

S 16° 15' W 
N15° 25'W 
N 28° 16' E 
S 49° 15' W 

S16° 20' W 
N17° 25' W 
N 27° 01' E 
N 50° 07' W 


Note.—I f there be no course in the survey in which 
the foreward and back sights agree, take the one in which 
they agree the nearest, and add half the difference of the 
bearings to the least, and treat the result as the true bearing. 


18. Kemark IV. In passing 
.over the course AB', the north¬ 
ing is found to be HB , and the 
departure, which is west, is repre¬ 
sented by AH. Of the course BO\ 
the northing is expressed by BG , 
and the departure, which is east, 
by GO. Of the course CD, the 
southing is expressed by Cl, and 
the departure, which is east, by 
CF. Of the course DA, the south- 


tst 



s 















SEC. III.] TRAVERSE TABLE. 105 

i 

ing is expressed by KA , and tbe departure, which is west, 
by DK. It is seen from the figure, that the sum of 
the northings is equal to HB A BG~ HG ] and that the 
sum of the southings is equal to Cl + KA =PA = IIG: 
hence, the sum of the northings is equal to the sum of the 
southings. 

If we consider the departures, it is apparent that the 
sum of the eastings is equal to GO A CF= GF\ and that 
the sum of the westings is equal to AHADK= GF\ hence 
also, the sum of the eastings is equal to the sum of the westings. 
We therefore conclude, that when any survey is correctly 
made, the sum of the northings will he equal to the sum of the 
southings , and the sum of the eastings to the sum of the 
westings. 

It would indeed appear plain, even without a rigorous 
demonstration, that after having gone entirely round a 
piece of land, the distance passed over in the direction due 
north, must be equal to that passed over in the direction 
due south; and the distance passed over in the direction 
due east, equal to that passed over in the direction due 
west. 

Having now explained the necessary operations on the 
field, we shall proceed to show the manner of computing 
the contents of the ground. We shall first explain, 


THE TRAVERSE TABLE AND ITS USES. 

19. This table shows the latitude and departure corres¬ 
ponding to bearings that are expressed in degrees and 
quarters of a degree from 0 to 90°, and for every course 
from 1 to 100, computed to two places of decimals. 

The following is the method of deducing the formulas 
for computing a traverse table; by means of these for¬ 
mulas and a table of natural sines, the latitude and depar¬ 
ture of a course may be computed to any desirable degree 
of accuracy. 


106 


ELEMENTS OF SURVEYING. [BOOK IL 


Let AD represent any course, and 
NAD — A CD, expressed in degrees and 
minutes, be its bearing. Let AC be the 
unit of measure of the course, and also 
the radius of the table of natural sines 
(Bk. I., Sec. III., Art. 14). Draw DE and 
CB parallel to NS, and AE perpen¬ 
dicular to AN. Then will DE be the 
latitude , and AE tlie departure of the course , and CB the co¬ 
sine, and AB the sine of the hearing. 

From similar triangles we have these proportions, 

AC : CB :: AD : DE, or 

1 : cos of the bearing : : course : latitude, 

AC : AB : : AD : AE, or 

1 : sin of the bearing : : course : departure. 

Whence, lat. = course X cos of the bearing, 
dep. = course X sin of the bearing. 

We have then the following practical rule for compu¬ 
ting the latitude and departure of any course. 

Look in a table of natural sines for the cosine and sine of 
the hearing. Multiply each hy the length of the course, and the 
first product will he the latitude, and the second will he the 
departure of the given course. 



EXAMPLES. 

1. The bearing is 65° 39', the course 69.41 chains: what 
is the latitude, and what the departure? 

Natural cosine of 65° 39'.41231 

Length of the course.*. . . 69.41 

Product, which is the Dif. of Latitude, 28.6184371. 

Natural sine of 65° 39'.■ .91104 

Length of the course.69.41 

Product, which is the Departure . . 63.2352864. 














I 


SEC. III.] 


TRAVERSE TABLE. 


107 


2. The bearing is 75° 47', the course 89.75 chains: what 
is the latitude, and what the departure? 

Natural cosine of 75° 47'.24559 

Length of course.89.75 

Product, which is the Dif. of Latitude, 22.0417025. 

Natural sine of 75° 47'.96937 

Length of course.89.75 

Product, which is the Departure . . 87.0009575. 

20. In this manner the traverse table given at the end 
of the book has been computed. When the bearing is 
given in degrees and quarters of a degree, and the differ¬ 
ence of latitude and departure are required to only two 
places of decimals, they may be taken directly from the 
traverse table. 

If the bearing is less than 45°, the angle will be found 
at the top of the page; if greater, at the bottom. Then, 
if the distance is less than 50, it will be found in the col¬ 
umn “distance,” on the left hand page; if greater than 50, 
in the corresponding column of the right hand page. 

The latitudes or departures of courses 
of different lengths, but which have the 
same bearing, are proportional to the 
lengths of the courses. Thus, in the 
figure, the latitudes AG, AG , or the de¬ 
partures GF, CB , are to each other as 
the courses AF, AB. S 

Therefore, when the distance _ is greater than 100, it 
may be divided by any number which will give an exact 
quotient, less than 100 : then the latitude and departure of 
the quotient being found and multiplied by the divisor, the 
products will be the latitude and departure of the whole 
course. It is also*plain, that the latitude or departure of two 
or more courses, having the same bearing, is equal to the 
sum of the latitudes or departures of the courses taken sepa¬ 
rately. 

Hence, if we have any number greater than 100, as 
614, we have only to recollect that, 610 -f- 4 = 614; and 
also, that the latitude and departure of 610, are ten times 


w- 


c 

a 

r 


. 7 ) 

i 

-;F 

: i 

A 

J 


B 


E 


c 5 















108 


ELEMENTS OF SURVEYING. [BOOK II. 


as great, respectively, as tlie latitude and departure of 
61: that is, equal to the latitude and departure of 61 mul¬ 
tiplied by 10, or with the decimal point removed one place 
to the right. 


EXAMPLES. 


1. To find the latitude and departure for the bearing 
29J°, and the course 614. 


Latitude for 610 . 
Latitude for 4 . 

Latitude for 614 . 


530.90 

8.48 


Departure for 610 . 
Departure for 4 . 


534,38 


Departure for 614 . 


300.40 

1.97 

302.37 


In this example, the latitude and departure answering 
to the bearing 29^°, and to the’distance 61, are first taken 
from the table, and the decimal point removed one place 
to the right: this gives the latitude and departure for the 
distance 610; the latitude and departure answering to the 
same bearing and the distance 4, are then taken from the 
table and added. 


2. To find the latitude and departure for the bearing 
62|°, and the course 7855 chains. 


Latitude for 7800 
Latitude for 55 

Latitude for 7855 


3602.00 

25.40 

3627.40 


Departure for 7800 . 6919.00 
Departure for 55 . 48.79 

Departure for 7855 . 6967.79 


Eemark. When the distances are expressed in whole 

numbers and decimals, the manner of finding the latitudes 

§ 

and departures is still the same, except in pointing off the 
places for decimals: but this is not difficult, when it is re¬ 
membered that the column of distances in the table, may 
be regarded as decimals, by removing the decimal point to 
the left in the other columns. * 


3. To find the latitude and departure • for the bearing 
47f°, and the course 37.57. 


Latitude for 87.00 
Latitude for .57 

Latitude for 37.57 



Departure for 37.00 
Departure for .57 


25.26 


Departure for 37.57 


27.39 

.42 

2L81 























8 EC. III.] 


OF BALANCING. 


109 


OF BALANCING THE WORK. 

21. Tlic use of the traverse table being explained, we 
can proceed to compute the area of the ground. 

The field notes having been completed, rule a new table, 
as below, with four additional columns, two for latitude, 
and two for departure. 

Then find, from the traverse table, the latitude and de¬ 
parture of each course, and enter them in the proper col¬ 
umns opposite the station. 

Then add up the column of northings, and also the col¬ 
umn of southings: the two sums should be equal to each 
other. If they are not, subtract the less from the greater; 

the remainder is called the error in latitude. This error 

\ 

takes the name of that column which is the less. For 
example, if the sum of the northings is less than the sum 
of the southings, the error is called, error in northing: but 
if the sum of the southings is less than the sum of the 
northings, the error is called, error in southing. We find 
the error for each particular course by the following pro¬ 
portion. 

As the sum of the courses 
Is to the error of latitude, 

So is each particular course 
To its correction. 

The error thus found may be entered in a separate col¬ 
umn ; after which add it to the latitude of the course when 
the error and latitude are of the- same name , but subtract 
it when they are of different names. This will make the 
sum of the northings equal to the sum of the southings, 
and is called balancing the work. The northings and south 
ings thus corrected are entered in columns on the right, 
under the head balanced. 

0 

The eastings and westings are balanced in the same 
manner; the difference between their sums being called 
error in departure. 

For an example, we will resume the one already con¬ 
sidered. 


110 


ELEMENTS OF SURVEYING. 


[BOOK II 





LATITUDE. 

DEPARTURE. 



BALANCED. 

Sta. 

Bearings. 

Distan¬ 

ces. 

N. 

+ 

S. 

E. 

+ 

W. 

Cor. 

Lat. 

Cor. 

Dep. 

N. 

+ 

S. 

E. 

+ 

W. 

1 

N 31W 

10. 

8.53 



5.22 

+ 0.18 

+ 0.02 

8.71 



5.24 

2 

N G2J° E 

9.25 

4.23 


8.22 


+ 0.17 

— 0.01 

4.40 


8.21 


3 

S 36° e 

7.C0 


G.15 

4.47 


— 0.14 

— 0.01 


6.01 

4.46 


4 

S 45^0 w 

10.40 


7.29 


7.41 

—0.19 

+ 0.02 


7.10 


7.43 

Sum of courses, 37.25 

12.76 

13 44 
12.76 

12 0t» 

12.G3 

12.63 

13.11 

13.11 

12.G7 

12.67 


Error in Northing 


0.G8 


0.0G Error in Westing. 


As 37.25 : 0.68 : : 10 : 0.18 error in lat. of 1st course 

As 37.25 : 0.68 : : 9.25 : 0.17 error in lat. of 2d course. 

As 37.25 : 0.68 :: 7.60 : 0.14* error in lat. of 3d course. 

As 37.25 : 0.68 :: 10.40 : 0.19 error in lat. of 4tli course. 

As 37.25 : 0.06 : : 10 : 0.02* error in dep. of 1st course. 

As 37.25 : 0.06 :: 9.25 : 0.01 error in dep. of 2d course. 

As 37.25 : 0.06 : : 7.60 : 0.01 error in dep. of 3d course. 

As 37.25 : 0.06 : : 10.40 : 0.02 error in dep. of 4th course. 

22. Bemark I. In finding the error in latitude or de¬ 
parture, for a particular course, the last figure is sometimes 
doubtful: in which case it is best to -mark it, as in the 
third proportion for error in latitude, and the first for er¬ 
ror in departure; and then, if the figures taken do not 
balance the work, let each be increased or diminished by 1. 

23. Bemark II. It has already been observed (Art. 18), 
that if the measurements on the field be correctly made, 
the sums of the northings and southings will be equal to 
each other, as also those of the eastings and westings. It 
is the opinion of some surveyors, that when the error in 
latitude or departure exceeds one link for every five chains 
of the courses, the field notes ought not to be relied on. 

_ V 

This, perhaps, is a higher degree of accuracy than can be 
attained. The error, however, should always be made 
considerably less than one link to a chain. 

24. The following is an example in which the latitude 
and departure of each course have been computed from 
the table of natural sines. 















































SEC. III.] 


OF BALANCING. 


Ill 


Sta. 

Bearings. 

Dist. 

Dif. of Latitude. 

Departure. 

Balanced. 

N. 

S. 

E. 

VV. 

N. 

S. 

E. 

* W. 

1 

O > 

N 45 55 W 

53 ch. 

36.81210 



38.07149 

36.65908 



38.01149 

2 

N 4 50 E 

14.40 

74.13513 


6.26S94 


73.12813 


6.26894 


3 

N S9 05 E 

125.50 

2.00800 


125.48368 


1.96126 


125.49228 


4 

S 1 50 W 

11.80 


11.16338 


2.29688 


72.11110 


2.296S8 

5 

S 1 40 E 

31.20 


30.92101 

4.16239 



31.12138 

4.16239 


6 

N 89 25 W 

35.50 

0.36139 



35.49322 

0.36139 



35.49822 

7 

S 84 35 W 

40. 


3.11600 


39.82120 


3.80352 


39.81260 

8 

S 14 35 W 

21. 


5.58264 


20.24442 


5.613S5 


20.24442 


113.31662 

112.04309' 

112.04309 

135.91501 

135.93221 

135.91501 

112.10986 

112.10985 

135.92361 

135.92361 


Error in Southing 1.33353 0.01120 Error in Easting. 

Half Error 0.66616 0.00860 Half Error. 


Instead of balancing by the method just explained, we 
divide each error by two. Now if we subtract half the 
error in southing from the column of northings, and at the 
same time add it to the column of southings, these two 
columns will exactly balance. In like manner, if we sub¬ 
tract half the error in easting from the column of westings, 
and at the same 'time add it to the column of eastings, 
these columns will also balance. 

The errors should be distributed in proportion to the 
lengths of the courses, but this may be done with sufficient 
accuracy without making the proportions. If any of the 
courses have been run over rough ground, the probability 
is that the errors belong to these courses, and they should 
be distributed among them. 

In this example we separate the half error in southing 
into the three parts .40700, .21802, and .04674, and subtract 
them respectively from the northings of courses 2, 1, and 
8, and then place the northings in the balanced columns. 
For the southings we separate the half error into the four 
parts .40772, .20031, .03121, and .02752, and add them respec¬ 
tively to the southings of the courses 4, 5, 8, and 7. We 
then enter the southings in the balanced columns. As the 
error in easting is so small, we add half of it to the east¬ 
ing of course 3, and subtract half from the westing of 
course 7. 










































112 


ELEMENTS OF SURVEYING. [BOOK II 


OF THE DOUBLE MERIDIAN DISTANCES OF THE COURSES. 

25. After tlie work lias been balanced, the next thing 
to be done is to calculate the double meridian distance of 
each course. 

For tliis purpose, a meridian line is assumed, lying 
either wholly without the land, or passing through any 
point within it. It is, however, most convenient to take 
that meridian which passes through the most easterly or 
westerly station of the survey; and these two stations are 
readily determined by inspecting the field notes. 

Having chosen the meridian, let the station through 
which it passes, be called the principal station , and the 
course which begins at this point, the first course. Care, 
however , must be taken, not to confound this with the course 
which begins at station 1, and which is the first course that is 
entered in the field 7iotes. 

It has already been remarked (Art. 10), that all de¬ 
partures in the direction east, are considered as plus , and 
all departures in the direction west as minus. 

26. To deduce a rule for finding the double meridian 

distances of the courses. Let BC 
represent any course, and AB the 
preceding course; also, let D and 
E be their middle points. Draw 

Elf CM, and DG, perpendicular to 
the assumed meridian NS. Draw 

also A I, EK, and BL , parallel to 
NS. Then 2 DG is the double me¬ 
ridian distance of the course BC\ 
and 2EH=2KG, is the double me¬ 
ridian distance of the course AB. 

Now, 2 DG — 2 GK + 2AZ- + 2 LD ; but 2 KL = IL is the 
departure of the course AB, and 2 LD — MC is the depar¬ 
ture of the course BC ; 

consequently, 2 GD = 2 GK -f IL + MC ; 

hence, the double meridian distance of a course, is equal 
to the double meridian distance of the preceding course 


N 







SEC. Ill] DOUBLE MERIDIAN DISTANCES. 


113 


plus the departure of that course plus the departure of the 
course itself; if there is no preceding course, the first 
two terms become zero. We therefore have the following 

RULE. 

I. The double meridian distance of the first course is equal 
to its departure. 

II. The double meridian distance of the second course is 
equal to the double meridian distance of the first course , plus 
its departure , plus the departure of the second course. 

III. The double meridian distance of any course is equal 
to the double • meridian distance of the preceding course , plus 
its departure , plus the departure of the course itself. 

27. Remark. It should be recollected that plus is here 
used in its algebraic sense, and that when the double me¬ 
ridian distance of a course and the departure which is to 
be added to it, are of different names, that is, one east and 
the other west, they will have contrary algebraic signs ; 
hence, their algebraic sum will be expressed by their dif¬ 
ference, with the sign of the greater prefixed to it. 

If the assumed meridian cuts the enclosure, the double 
meridian distances, estimated to the left, must be taken 
with the minus sign. 

• The double meridian distance of the last course should 
be equal to the departure of that course. A verification 
of the work is, therefore, obtained by comparing this double 
• meridian distance with the departure of the course. 

28. To apply the above rule to the particular example 
already considered (Art. 21), rule a new table as below, in 
which are entered the balanced northings and southings, and 
the balanced eastings and westings. 

In this table there is but a single column for the dif¬ 
ferences of latitude, and a single column for the departures. 
The + sign shows when the difference of latitude is north, 
and the — sign when it is south. The 4- sign also shows 
when the departure is east, and the — sign when it is west. 

8 


114 


ELEMENTS OF SURVEYING. [BOOK II. 


Sta. 

Bearings. 

Distances. 

Dif. Lat. 

Dep. 

D. M. D. 

1 

1ST 81i° W 

10. 

+ 8.71 

-5.24 

+17.91 

— 7.43 

— 5.24 





+ 5.24 

2* 

N 62|° E 

9.25 

+ 4.40 

+ 8.21 

8.21 

8 

S 36° E 

7.60 

-6.01 

+ 4.46 

+ 8.21 
+ 8.21 
+ 4.46 

4 

S 451° W 

10.40 

-7.10 

■- 7.43 

+ 20.88 

* +20.88 
+ 4.46 
— 7.43 






+ 17.91 


We see, from inspecting the notes, that 2 is the most 
westerly, and 4 the most easterly station. Either of them 
may, therefore, be taken for the principal station. Let us 
assume 2 for the principal station, and distinguish it by a 
star, thus *. 

Having done so, we enter the departure 8.21 in the 
column of double meridian distances, which gives the 
double meridian distance of the first course. The double 
meridian distances of the other courses are calculated ac¬ 
cording to the rule; and as the last, opposite to station 1, 
is equal to the departure of the course, the work is known 
to be right. 

29. Having shown the manner of computing the double 
meridian distance of each course, we shall now deduce a 
rule for finding the 

AKE A. 


Let us still consider the same 
example. We will first write the 
differences of latitude and the 
double meridian distances of the 
courses, in the following table. 


1ST 



























THE AREA. 


115 


SEC. Ill] 


r 

Stations. 

-Dif. of Latitude. 

D. M. D. 

Area. 

'+ 

Area. 

1 

+ cB 

+ 2 ba 

2 cAB 


2* 

+ Bs 

+ 2 qp 

2BsC 

• 

3 

-yD 

+ 2nh 


2ms CD 

4' 

~Df 

+ 2 ed 


2cmDA 


It is evident, that cB multiplied by 2ba = cA, will give 
double the area of the triangle cAB. But cB and ba are 
both plus; hence, the product will be plus, and must be 
put in the column of plus areas. Double the area of 
the triangle BsC, is equal to Bs multiplied by 2 qp, which 
product is also plus. 

The area of the trapezoid ms CD is equal to yD = ms 
multiplied by nh (Geom., Bk. IV., Prop. VII., S.); hence, 
double the area is equal to yD into 2 nh. But since yD is 
minus, and 2 nh plus, it follows that the product will be 
negative; hence, it must be placed in the column of nega¬ 
tive areas. 

Double the area of the trapezoid cADm , is equal to 
Df—mc multiplied by 2 de: but, since Df is negative and 
2 de positive, the product will be negative. 

It is now evident that the difference between the two 
columns is equal to twice the contents of the figure A BCD: 
and since the same may be shown for any other figure, we 
may write, for finding the areas, the following general 

RULE. 

I. Multiply the double meridian distance of each course by 
its northing or southing , observing that like signs in the multi¬ 
plicand and multiplier give plus in the product , and that un¬ 
like signs give minus in the product. 

II. Place all the products which have .a plus sign , in one 
column , and all the products which have a minus sign , in an¬ 
other. 

III. Add up the columns separately and take the difference 
of their sums: this difference will be double the area of the land. 












116 


ELEMENTS OF SURVEYING. 


[BOOK II. 


30. We will now make tlie calculations in numbers. 
Having balanced the work, we can place it in tlie follow¬ 
ing table. 


Sta. 

Bearings. 

Dist. 

Dif. Lat. 

Dep. 

D. 

M. D. 

Area. 

+ 

Area. 

1 

N 

340 w 

10 . 

+ 8.71 

— 5.24 

+ 

5.24 

45.6404 


2 * 

N 

62JO E 

9.25 

+ 4.40 

+ 8.21 

+ 

8.21 

36.1240 


3 

S 

360 e 

7.60 

— 6.01 

+ 4.46 

+ 

20.88 


125.4888 

4 

S 

45£0 w 

10.40 

— 7.10 

— 7.43 

+ 

17.91 


127.1610 


81.7644 

252.6498 


81.7644 

2)170.8854 

Area in square chains .... 85.4427 

Dividing by 10 . 8.54427 

4 

2.17708 

40 

.flns. 8^. 2 R. 7 P . 7.08320 

Observing in tke field notes that station 2 is the most 
westerly point of the land, we assume the meridian which 
passes through this point, as the one from which the me¬ 
ridian distances are to be calculated’. We mark the prin¬ 
cipal station with a star. 

Opposite station 2, we enter, in the column of double 
meridian distances, headed D. M. D., the departure of the 
course from 2 to 3, which is the double meridian distance 
of that course, and plus. To this we add the departure 
of the course, and also the departure of the next course: 
their sum is the double meridian distance of the course 
from 3 to 4. 

To the last sum add the departure opposite station 3, 
and the minus departure opposite station 4: their algebraic 
sum is the double meridian distance from 4 to 1. 

To the last sum add the last departure, which is minus, 
also the next departure which is likewise minus: this will 
give the double meridian distance of the course from 1 to 
2, which is equal to its departure. 

Then forming the products, adding them together, ta¬ 
king their difference, and dividing it by 2, according to 
the rule, we obtain the contents of the ground. 






























SEC. Ill] 


OF PLOTTING. 


117 


OF PLOTTING. 


81. It only remains to make 
a plot of the ground. 

For this purpose, draw any 
line, as US, to represent the me¬ 
ridian passing through the princi¬ 
pal station; and on this line take 
any point, as B , to represent that 
station. 


N 



FIRST METHOD. 

Haying fixed upon the scale on which the plot is to be 
made, lay off from B on the meridian, a distance Bs equal 
to the difference of latitude of the first course, and at s 
erect a perpendicular to the meridian, and make it equal 
to the departure of the first course: then draw BO\ which 
will be the first course. 

' Through C draw a meridian, and make Cf equal to the 
difference of latitude of thev second course, and through / 
draw a perpendicular /D, and make it equal to the depar¬ 
ture of the second course: draw CD , and it will be the 
second course. 

Lay down, in the same manner, the courses DA and 
AB\ and the entire plot will be completed. 

SECOND METHOD. 

The work may be plotted in another manner, thus. 
At the principal station B, lay off an angle equal to the 
bearing from B to (7, which will give the direction of BC. 
Then, from the scale of equal parts, make BC equal to the 
first course, this will give the station C. 

Through C draw a meridian, and lay off an angle equal 
to the bearing from C to D , and then lay off the course 
CD. Do the same for the bearing at D and the course 
DA ; also, for the bearing at A and the course AB ) and a 






118 


* 


ELEMENTS OF SURVEYING. [BOOK II. 





complete plot of tlie ground will thus be obtained. If the 
work is all right ; the last line AB will exactly close the 
figure. This plot is made on a scale of 10 chains to an inch. 

1. It is required to determine the contents and plot of a 
niece of land, of which the following are the field notes, viz. 


Stations. 

Bearings. 

Distances. 

1 

1ST 46i° W 

20 ch. 

• 

2 

N 51f° E 

13.80 

3 

E 

21.25 

4 

S 56° E 

27.60 

5 

S 33i° W 

18.80 

6 

hT 74J° w 

30.95 


CALCULATION. 


Sta¬ 

tions. 



Dif. 

Lat. 

Dep. 

BALANCED. 




Bearings. 

Dis. 

N 

+ 

s. 

Ev 

+ 

W 

Lat. 

Dep. 

D.M.D. 

+ 

AREA. 

+ 

AREA. 

1 

N 46i° W 

20 ch 

13.77 



14.51 

+13.88 

—14.56 

14.56 

202.0928 


2* 

N 51f° E 

13.80 

8.54 


10.84 


+8.61 

+10.81 

10.81 

93.0741 


3 

E 

21.25 



21.25 



+21.20 

42.82 

• 


4 

S 560 e 

27.60 


15.44 

22.88 

A 

—15.29 

+22.82 

86.84 


1327.7836 

5 

S 33p W 

18.80 


15.72 


10.31 

—15.63 

—10.36 

99.30 


1552.0590 

6 

N 74p YV 

30.95 

8.27 



29.83 

+8.43 

—29.91 

59.03 

497.6229 


Sum of courses 132.40 

30.58 

31.16 

30.58 

54.97 

54.65 

54.65 




792.7898 2879.8426 
792.7893 


Error in northing .. 0.58 0.32 Error in Westing 2)2087.0528 


Jins. 104./3 1/2 16P. 1043.5264 

Plot of the example. 



s 



















































SEC. Ill] 


PROBLEMS. 


119 


32. Remark. When a bearing is due east or west, the 
error in latitude # is nothing; the course must then be sub¬ 
tracted from the sum of the courses, and the remainder 
taken in balancing the columns of latitude. In the last 
example, the 3d bearing is due east, and the first term of 
the several proportions for error in latitude, was 132.40 — 
21.25 = 111.15. 

In like manner, if a bearing is due north or south, the 
error in departure is nothing; and the sum of the courses 
must be diminished by this course, before balancing the 
columns of departure. 

2. Required the contents, and plot of a piece of land, 
of which the following are the field notes. 


Stations. 

Bearings. 

Distances. 

1 

S 34° W 

3.95 ch. 

2 

S 

4.60 

3 

S 36^° E 

8.14 

4 

N 59£° E 

3.72 

5 

N 25° E 

6.24 

6 

1ST 16° W 

3.50 

7 

N65° W 

8.20 


Ans. 10A. OR. 5P. 


3. Required the contents and plot of a piece of land, 
from the following field notes. 


Stations. 

Bearings. 

Distances. 

1 

S 40° W 

70 rods 

2 

N 45° W 

89 

3 

N 36° E 

125 

4 

N 

54 

5 

S 81° E 

186 

6 

is 

o 

OO 

m 

137 

7 

W 

130 


Ans . 207 A. 3 R, 33 P. 
















120 


ELEMENTS OF SURVEYING. [BOOK IL 


4. Required the contents and plot of a piece of land, 
from the following field notes. 


Stations. 

Bearings. 

Distances. 

1 

S 40}° E 

31.80 ch. 

2 

1ST 54° E 

2.08 

3 

N 29}° E 

2.21 

4 

N 28|° B 

35.35 

5 

N57° W 

21.10 

6 

S 47° W 

31.30 


Ans. 92 A. SB. 32 R 


5. Required the area of a survey of which the follow¬ 
ing are the field notes. 


Stations. 

Bearings. 

Distances. 

1 

1ST 42° E 

5.00 ch. 

2 

East. 

4.00 

3 

N 9 s E 

4.00 

4 

S 69° E 

5.56 

5 

S 36° E 

7.00 

6 

S 42° W 

4.00 

7 

S 75° W 

10.00 

8 

N 39° W 

7.50 


If, in this example/ we assume 1 as the principal sta¬ 
tion, the double meridian distances will all be plus, and 
the positive area will exceed the negative. 

In balancing we shall find the error in southing to be 
.28 ch. and in westing .22 ch. The area is 13 A. 0 B. IIP. 
It should however be remarked, that in all the examples 
the answers may be slightly varied by distributing the 
corrections. 

6. What is the area of a survey of which the following 
are the field notes. 














SEC. Ill] 


PROBLEMS. 


121 


Stations. 

Bearings. 

Distances. 

1 

N 75° 00' E 

54.8 rods. 

✓ 2 

N 20° 30' E 

41.2 

3 

East. 

64.8 

4 

S 33° 30' W 

141.2 

' 5 

S 76° 00' W 

64.0 

6 

North. 

36.0 

7 

£ 

o 

o 

o 

00 

m 

46.4 

8 

N 53° 15' W 

46.4 

9 

N 36° 45' E 

76.8 

10 

N 22° 30' E 

56.0 

11 

S 76° 45' E 

48.0 

'*12 • 

S 15° 00' W 

43.4 

13 

S 16° 45' W 

40.5 

_ 


In this survey 4 is the most easterly and 9 the most 
westerly station. The area is equal to 110A. 2 R. 23 P. 
It may vary a little, on account of the way in ‘which the 
balancing is done. 

7. What are the contents of a piece of land of which 
the following are the field notes? 


Stations. 

Bearings. 

Distances. 

1 

S 75° W 

13.70 ch. 

2 

S 20J° W 

10.30 

3 

West. 

16.20 

4 

N 33}° E 

35.30 

5 

N 76° E 

16.00 

6 

South. 

9.00 

7 

N 84° E 

11.60 

8 

S 53i° E 

11.60 

9 

S 36f° W 

19.20 

10 

S 22}° W 

14.00 

11 

1ST 76J° W 

12.00 

12 

N 15° E 

10.85 

13 

1ST 161° E 

10.12 











122 


ELEMENTS OF SURVEYING. [BOOK IL 


In this survey 4 is the most westerly station and 9 the 
most easterly. The area is 110A. 2 R. 23 P. The result 
may, however, as in the other examples, be slightly varied 
by the balancing. 

8. What is the area of a survey of which the following 
are the notes? 


Stations. 

Bearings. 

Distances. 

1 

S 46J° E 

80 rods 

2 

S 5ir W 

55.20 

3 

West. 

85 

4 

N 56° W 

110.40 

5 

N 33i° E 

75.20 

6 

S 74J° E 

123.80 


Ans 104A IP. 16P. 


I. To determine the contents and boundary of a piece of land, 
by means of offsets from the principal lines. 

33. An offset is a line measured perpendicular to a 
course, and may lie either on the right or left of it. 

Let ABODE be a piece of 
ground to be surveyed. Let us 
suppose it to be bounded on the 
west and north by a fence and 
road, and on the east and south 
by a creek or river. 

Assume as stations the prin¬ 
cipal points A, B ) C, D, and E. 

Take, with the compass, the bear¬ 
ings from A to P, from B to C, 
from C to D, from D to E, and 
from E to A\ and measure the dis¬ 
tances AB, BC,\ CD, DE, and EA. 

At convenient points of the course AB, as a, c, and f 
measure the offsets ab, cd , fg. Then, having measured 
these lines, as also the distances Aa, ac, cf and fB, enough 













SEC. III.] 


PROBLEMS. 


123 


will be known to determine the area winch lies without the 
station line AB. The points b, d and g, of the fence which 
runs from A to B ) are also determined. 

Erect, in a similar manner, offsets to the other courses, 
and determine the areas which lie without the station lines. 
These several areas being added to the area within the 
station lines, will give the entire area of the ground. 

If the offsets fall within the station lines, the corres¬ 
ponding area must be subtracted from the area which is 
bounded by the station lines. 

II. To determine the bearing and distance from one point to 
another, when the points are so situated that one cannot be 
seen from the other. 

34. Let A and 0 be the two 
points, and AB a meridian pass¬ 
ing through one of them. From 
either of them, as A, measure a 
course A2, of a convenient length 
in the direction towards C, and 
take the bearing with the com¬ 
pass. At 2, take the bearing of 
a second course, and measure the 
distance to 3. At 3, take a third 
bearing and measure to 4. At 
4, take the bearing to C , and 
measure the distance from 4 to C. 

Then, the difference between the sum of the northings 
and the sum of the southings will be represented by AB, 
and the difference between the sum of the eastings and 
the sum of the westings by BO. The base AB, and the 
perpendicular BO of the right-angled triangle ABO, are then 
known. The angle at the base, BAO, is the bearing from 
A to 0; or the equal alternate angle at 0 is the bearing 
from 0 to A, and the hypothenuse A 0 is the distance. 

35. Having measured the bearings and courses on the 
field, form a table, and find the base and perpendicular 
of the right-angled triangle, in numbers. 






124 


ELEMENTS OF SURVEYING. [BOOK IL 


Stations. 

Bearings. 

Distances. 

• 

N. 

s. 

E. 

w. 

1 

N 61° W 

40 ch 

19.39 



34.98 

2 

1ST 42° W 

41. 

30.47 



27.43 

3 

N 12° E 

16.10 

15.75 


3.35 


4 

1ST 47° E 

32.50 

22.16 


23.77 



• 

AB 

= 87.77 


27.12 

62.41 


27.12 

CB = 35.29 oh. 


Eemark. Had any of tlie 
courses run south, AB would have 
been equal to the sum of the 
northings, minus the sum of the 
southings. 

To find the angle BAG\ or the 
bearing from A to 0. 

As radius : tan A : : AB : B 0, 
or AB : BO : : R : tan A : 
that is, 



As AB 87.77 . ar. comp. 

: BO 85.29 . 


: tan A 21° 54' 12" 

To find the distance AO. 
As sin A 21° 54' 12" ar. comp. 

• II ...... 

: : BO 85.29 .... 

: AO 94.6 . 


8.056654 

1.547652 

10 . 

9.604306 


0.428242 

10 . 

1.547652 

1.975894 


Hence, the bearing and distance are both found. 


OF SUPPLYING OMISSIONS IN THE FIELD NOTES. 

36. The last problem affords an easy method of finding 
the bearing and length of one of the courses of a survey, 
































SEC. Ill] 


PROBLEMS. 


125 


when the bearings and lengths of all the others are known. 
It may be necessary to use this method when there are 
obstacles which prevent the measuring of a course, or when 
the bearing cannot be taken. Indeed, two omissions may 
in general be supplied by calculation. It is far better, 
however, if possible, to take all the notes on the field. 
For, when any of them are supplied by calculation, there 
are no tests by which the accuracy of the w*ork can be as¬ 
certained, and all the errors of the notes affect also the 
parts which are supplied. 


1. In a survey we have the following notes: 


Stations. 

Bearings. 

Distances. 

1 

2 

3 

4 

N 31i° W 
hr 62J° E 

Lost. 

S 45|° W 

10 ch. 

9.25 

Lost. 

10.40 


What is the bearing and distance from station 3 to 4 ? 

A j Bearing, S 38° 52' E. 
US ’ ( Distance, 7.03 ch. 


2. In a survey we have the following notes: 


Stations. 

Bearings. 

Distances. 

1 

S 40J° E 

31.80 ch. 

2 

N 54° B 

2.08 

3 

Lost. 

Lost. 

4 

hr 28f° E 

35.35 

5 

N57° W 

21.10 

6 

S 47° W 

31.30 


What is the bearing and distance from 3 to 4 ? 

(Bearing, N 84°'47' E. 
* \ Distance, 2.19 ch. 
















126 


ELEMENTS OF SURVEYING. [BOOK IL 


III. To determine the angle included between any two courses , 

when their bearings are known. 


37. Let NS be a meridian 
passing through A. 

Let AB, A C, AH, AD ) and 
AF, be five courses running 
from A. We readily deduce 
the following 




PRINCIPLES. 


AC is N 26° W 
AH is N 65° W 

CAH— 39° 


When the meridional letters 
are alike, and those of depar¬ 
ture also alike, the difference of 
the bearings is the angle between 
the courses. 


AB is N 46° B 
AC is N 26° W 

CAB = 72° 


When the meridional letters 
are alike, and those of depar¬ 
ture unlike, the sum of the bear¬ 
ings is the angle between the 
courses. 


AC is N 26° W 
AD is S 66° W 

CAD = 180°- 92°= 88° 


AC is N 26° W 
AF is S 66° E 

CAF= 180°- 40°= 140° 


When the meridional letters 
are unlike, and those of depar¬ 
ture alike, the angle between the 
courses is equal to' 180°, minus 
the sum of the bearings. 

When the meridional letters 
are unlike, and those of depar¬ 
ture also unlike, the angle be¬ 
tween the courses is equal to the 
difference of the bearings taken 
from 180°. 


Remark. The above principles are determined, under the 
supposition that the two courses are both run from the 
angular point. Hence, if it be required to apply them to 








SEC. III.]* 


OF DIVIDING LAND. 


127 


two courses run in the ordinary way, as we go around the 
field, the bearing of one of them must be reversed before 
the calculation for the angle is made. 

1. The bearings of two courses, from the same point, 
are N 37° E, and S 85° W: what is the angle included 
between them ? 

Ans. 182°. 

2. The bearings of two adjacent courses, in going round 
a piece of land, are N 39° W, and S 48° W: what is the 
angle included between them? 

Ans. 87°. 

* 

3. The bearings of two adjacent courses, in going round 
a piece of land, are S 85° W, and N 69° W: what is the 
angle included between them? 

Ans. 154°. 

4. The bearings of two adjacent courses, in going round 
a piece of lsfrid, are 1ST 55° 30' E, and S 69° 20' E : what 
is the angle included between them? 

Ans. 124° 50'. 


OF DIVIDING LAND. 

38. Fields are so variously shaped that it is difficult 
to give rules that will apply to all cases. It is by practice 
alone that facility is obtained in that branch of survey¬ 
ing relating to the division of estates. We shall add only 
a few examples that may serve as general guides in the 
application of the principles of Plane Geometry to such 
cases as may arise. 

I. To run a line from the vertex of a triangular field which 
shall divide it into two parts , having to each other the 
ratio of M to N. 

39. Let ABO be any triangular field. 

Divide the side BO into two 

parts, such that (Geom., Bk. IV., 

Prob. 1.) 

BD : DO : : m : n ; 
and draw the line AD: 

then will, ABD : DAO : : m : n. 


A 





128 


ELEMENTS OF SURVEYING. gBOOK II. 


For, the two triangles ABB , ADO having the same alti¬ 
tude are to each other as their bases (Geom., Bk. IV., P. 6, 
C.): hence, the triangle is divided into parts having the 
ratio of m to n. 


II. To run a line parallel to one side of a triangular field , 
that shall form with the parts of the two other sides a 

triangle equivalent to the ~ part of the field. 

40. Let CBA represent a triangular field and OA the 
side parallel to which the dividing line is to be drawn. 


On the side BO describe 
a semicircle : then divide BO 
at B , so that 

BD : BO : : m : n. 



At B , erect the perpendicular DG to the diameter BO } 
and draw BG. Then, with B as a centre, and as a 
radius, describe the arc of a circle cutting BO at E. 
Through E draw EF parallel to OA 1 and it will divide the 
triangle in the required ratio. 

For, (Geom., Bk. IV., P. 23.) 

W =BE° = BOX BD : 


or. 


BB 


BE 2 = BO 2 X ; whence, 

: : BD 


BE~ : BG : : BD : BO : : m : n. 
But, since the triangles BEF\ BOA are similar, 
BE~ : BO° : : BEF 
Wherefore, from equality of ratios, 

BEF : BOA : : m 


BOA. 


n 


and 


m 

BEF=-xBOA. 

t (/ 


Remark. The points E and F may easily be found 
by computation. 


For, since BE' = BOX BD. and BD = ~ X BC 

n 1 













8E0. Ill] 


OF DIVIDING LAND. 


129 


we have 


BE 2 = BC 2 X 


m 
n > 


or BE= BG 



In like manner 


BF= 



EXAMPLE. 


Let it be required to divide the trian¬ 
gular field GAB , in which AC— 9 ch. AB — 
11 ch. and GB — 7 ch. into two such parts 
that ABE shall be one-fourth of the whole 
field. 

In this case, we have 
m— 1, n = 4, and \F^ = " ^ ^ 




hence, 


n *42 
AE= 4 ch. 50 1. and AZ) = 5_ch. 501. 


III. To run a line from a given point in the boundary of a 
piece of land , so as to cut off, on either side of the line , 
a given portion of the field. 

41. Make a complete survey of the field, by the rules 
already given. Let us take, as an example, the field whose 
area is computed at page 118. That field contains 104^4 
1 R 16P, and the following is a plot of it. 



Let it now be required to run a line from station A , 
in such a manner as to cut off on the left any part of the 

field; say, 2 6A 2 R 31 P. 

9 









130 


ELEMENTS OF SURVEYING. [BOOK IL 


It is seen, by examining tlie field, that the division line 
will probably terminate on the course CD. Therefore, draw 
a line from A to (7, which we will call the first closing 
line. 

The bearings and lengths of the courses AB , BC, are 
always known; and in the present example are found in 
the table on page 118: hence, the bearing and distance 
from C to A , can be calculated by Art. 35: they are in 
this example, 

Bearing S 9° 28' E : Course 22.8 ch. 

• Having calculated the bearing and length of the closing 
line, find, by the general method, the area which it cuts 
off: that area, in the present case, is 

ISA 3 R SR 

It is now evident that the division line must fall on 
the right of the closing line AC, and must cut off an area 
ACH, equal to the difference between that already cut off, 
and the given area: that is, an area equal 

2 6A 2 R 31P given area, 

13A 3 R 3 P area already cut off, 

to . . . 12A 3 R 28 P. 


Since the bearing of the next course CD, and the bear¬ 
ing of the closing line AC are known, the angle ACD 
which they form with each other, can be calculated, and is 
in this example 80° 32°. Hence, knowing the hypothenuse 
AC, and the angle ACC at the base, the length AG of 
the perpendicular let fall on the course CD, can be found, 
and is 22.49 chains. 

Since the area of a triangle is equal to its base multi¬ 
plied by half its altitude, it follows, that the base is equal 
to the area divided by half the altitude. Therefore, if the 
area 

12A 3 R 28P 

be reduced to square chains, and divided by 11.24^ chains, 
which is half the perpendicular A G, the quotient, which is 
11.58 chains, will be the base CH. Hence, if we lay off 
from C, on CD, a distance CH, equal to 11.58 chains, and 




SEC. IV.] 


PUBLIC LANDS. 


131 


tlien run the line AH, it will cut off from the land the re¬ 
quired area. 

Remark I. If the part cut off by the first closing line, 
should exceed the given area, the division line will fall on 
the left of AG. 

Remark II. If the difference between the given 
area and the first area cut off, divided by half the per¬ 
pendicular AG, gives a quotient larger than the course 
CD; then, draw a line from A to D, and consider it as 
the first closing line, and let fall a perpendicular on DE. 

Remark III. When the point from which the divi¬ 
sion line is to be drawn, falls between the extremities 
of a course, dividing the course into two parts, con¬ 
sider one of the parts as an entire course, and the other 
as forming a new course, having the same bearing. The 
manner of making the calculation will then be the same 
as before. 


SECTION IV. 

PUBLIC LANDS—VARIATION OF THE NEEDLE. 

1. Soon after the organization of the present govern¬ 
ment, several of the states ceded to the United States large 
tracts of wild land, and these, together with the lands since 
acquired by treaty and purchase, constitute what is called 
the public lands, or public domain. Previous to the year 
1802, these lands were parcelled out without reference to 
any general plan, in consequence of which the titles often 
conflicted with each other, and in many^cases, several grants 
covered the same premises. 

In the year 1802, the following method of surveying 
the public lands, was adopted by Colonel Jared Mansfield, 
then surveyor-general of the North-Western Territory. 

2. The country to be surveyed is first divided by 
meridians, six miles distance from each other; and then 



132 


ELEMENTS OF SURVEYING. [BOOK II. 


again, by a system of east and west lines, also six miles 
from each other. The country is thus divided into equal 
squares, which are called townships. Hence, each township 
is a square, six miles on a side, and contains thirty-six 
square miles. 

« 

3. For the purpose of illustration, we have obtained 
from the general land office the accompanying map, which 
represents a considerable portion of the State of Arkansas. 

The principal meridian in this Survey is called the 5th 
meridian, and passes through the point of junction of the 
White river and the Mississippi. The principal base line, 
running east and west, intersects this meridian a little to the 
east of White river; and from the meridian and base line, 
reckoned from this point of intersection, all the ranges of 
townships are laid off. 

For example, 1 North, will apply to all the townships 
lying in the first row north of the base line: 1 South, will 
apply to all the townships in the first row south of the base 
line. Range 1 East, will apply to all the townships lying 
in the first row, east of the 5th meridian : and range 1 
West, will apply to all lying in the first row to the west 
of it. The small figures designate the rows of townships, 
reckoned north and south from the base line, and the 
ranges reckoned east and west from the 5th meridian. 
Thus, township 1 North, range 4 West, has its exact place 
designated, and may be immediately located. 

4. The principal meridians, and the principal base lines 
are established by astronomical observation, and the lines 
of subdivision run with the compass. 

For convenience in making surveys, and for the purpose 
of designating particular localities, a state or large tract, is 
often divided into parts called “Districts.” There are three 
such districts in the map before us, the boundaries of which 
are designated by the full dark lines. 

5. Each township is divided into equal squares, by me¬ 
ridians one mile apart, and by east and west lines at the 
same distance from each other. Hence, each township is 
divided into 36 square miles, each one of which is called 

























































































































































































































































































134 ELEMENTS OF SURVEYING. [BOOK IL 

a section. The sections of a township are numbered from 
1 to 36, beginning at the north-east angle, and each con¬ 
tains 640 acres. 

The diagram exhibits the 36 sections of a township. 

c J • 


> 


6 

5 

4 

3 

2 

1 - 

7 

8 

9 

10 

11 

12 

18 

17 

10 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

27 

26 

25 

31 

32 

33 

34 

35 

36 


To describe a section accurately, we say, section num¬ 
ber 5, in township number 4 north, in range 3d west of a 
known meridian; the one, for example, drawn through the 
mouth of White river. The description fixes precisely the 
place of the section. Go to the 3d range of townships, 
west of the known meridian, find township number 4 north, 
in this range, and lastly, section number 5 of that town¬ 
ship. The corners of the sections should be marked by 
permanent corner-posts, or by lines blazed on trees. 

6. The sections are divided into half sections, quarter 
sections, and even into eighths of sections. The following 
table shows the contents of a township, and its subdivi¬ 
sions : 


1 township = 36 sections = 23040 acres. 
1 section = 640 acres. 

\ section = 320 acres. 

■} section = 160 acres, 
section = 80 acres. 



















SEC. IY.] VARIATION OF THE NEEDLE. 


135 


VARIATION OF THE NEEDLE. 

7. The angle which the magnetic meridian makes with 
the true meridian, at any place on the surface of the earth, 
is called the variation of the needle at that place, and is east 
or west, according as the north end of the needle lies on 
the east or west side of the true meridian. 

8. The variation is different at different places, and 
even at the same place it does not remain constant for any 
length of time. The variation is ascertained by comparing 
the magnetic, with the true meridian. 

9. If we suppose a line to be traced through those 
points on the surface of the earth, where the needle points 
directly north, such a line is called the line of no variation. 
At all places lying on the east of this line, the variation 
of the needle is west; at all places lying on the west of 
it, the variation is east. 

10. The public is much indebted to Professor Loomis, 
for the valuable results of many observations and much 
scientific research, on the dip and variation of the needle, 
contained in the 39th and - 42 d volumes of Silliman’s 
Journal. 

The variation at each place was ascertained for the year 
1840; and by a comparison of previous observations and 
the application of known formulas, the annual motion, or 
change in variation, at each place, was also ascertained, and 
both are contained in the tables which follow. 

11. If the annual motion was correctly found, and con¬ 
tinues uniform, the variation at any subsequent period can 
be ascertained by simply multiplying the annual motion 
by the number of years, and adding the product, in the 
algebraic sense, to the variation in 1840. It will be ob¬ 
served that all variations west are designated by the plus 
sign ; and all variations east, by the minus sign. The an¬ 
nual motions being all west, have all the plus sign. 


136 


ELEMENTS OF SURVEYING. [BOOK IL 


12. Our first object will be to mark the line, as it was 
in 1840, of no variation. For this purpose we shall make 
a table of places lying near this line. 


PLACES NEAR THE LINE OF NO VARIATION. 


Place. 

Latitude. 

Longitude. 

Variation. 

An. Motion. 

A Point. 

O 

o 

53' 

CO 

O 

o 

13' 

0° 

o 

o 

+ 4'.4 

* 

Cleveland, O. 

41 

31 

81 

45 

-0 

19 

4.4 

Detroit, Mich. 

42 

24 

82 

58 

-1 

56 

4 

Mackinaw. 

45 

51 

84 

41 

-2 

08 

3.9 

Marietta, O. 

39 

30 

81 

28 

-1 

24 

4.3 

Charlottesville, V a. 

39 

02 

78 

30 

+ 0 

19 

3.7 

Charleston, S. C. 

32 

42 

80 

04 

-2 

44 

1.3 


At the point whose latitude is 40° 53', longitude 80° 
13', the variation of the needle was nothing in the year 
1840, and the direction of the line of no variation, traced 
north, was 1ST 24° 35' west. The line of no variation, pro¬ 
longed, passed a little to the east at Cleveland, in Ohio— 
the variation there being 19 minutes east. Detroit lay still 
further to the west of this line, the variation there being 
1° 56' east; and Mackinaw still further to the west, as 
the variation at that place was 2° 08' east. 

The course of the line of no variation, prolonged south¬ 
erly, was S 24° 35' E. Marietta, in Ohio, was west of this 
line—the variation there being 1° 24' east. Charlottesville, 
in Virginia, was a little to the east of it—the variation there 
being 19' west; whilst Charleston, in South Carolina, was on 
the west,—the variation there being 2° 44' east. 

From these results, it will be easy to see about where 
the line of no variation is traced in our own country. 

13. We shall give two additional tables: 

















SEC. IV.] VARIATION OF THE NEEDLE. 


137 


PLACES WHERE THE VARIATION WAS WEST. 


Places. 

Latitude. 

Longitude. 

Variation. 

An. Motion. 

Angle of Maine. 

o 

OO 

00' 

67° 

37' 

+ 19° 

30' 

+ 8'.8 

Waterville, Me. 

44 

27 

69 

32 

12 

36 

5.7 

Montreal. 

45 

31 

73 

35 

10 

18 

5.7 

Keesville, N. Y. 

44 

28 

73 

32 

8 

51 

5.3 

Burlington, Yt. 

44 

27 

73 

10 

9 

27 

5.3 

Hanover, 1ST. H. 

43 

42 

72 

14 

9 

20 

5.2 

Cambridge, Mass. 

42 

22 

71 

08 

9 

12 

5 

Hartford, Ct. 

41 

46 

72 

41 

6 

58 

5 

Newport, B. I. 

41 

28 

71 

21 

7 

45 

5 

Geneva, 1ST. Y. 

42 

52 

77 

03 

4 

18 

4.1 

West Point. 

41 

25 

74 

00 

6 

52 

4 

New York City. 

40 

43 

71 

01 

5~ 

34 

3.6 

Philadelphia. 

39 

57 

75 

11 

4 

08 

3.2 

Buffalo, N. Y. 

42 

52 

79 

06 

1 

37 

4.1 


PLACES WHERE THE VARIATION WAS EAST. 


Places. 

Latitude. • 

Longitude. 

Variation. 

An. Motion. 

Mouth of Colum -) 



• 





bia River. ) 

46° 

12' 

123° 

30' 

-21° 

40' 

Unknowa 

Jacksonville, Ill. 

39 

43 

90 

20 

8 

28 

+ 2'.5 

St. Louis, Mo. 

38 

37 

90 

17 

8 

37 

2.3 

Nashville, Tenn. 

36 

10 

86 

52 

6 

42 

2 

Louisiana, at 

29 

40 

94 

00 

' 8 

41 

1.4 

Mobile, Ala. 

30 

42 

88 

16 

7 

05 

' 1.4 

Tuscaloosa, Ala. 

33 

12 

87 

43 

7 

26 

1.6 

Columbus, Geo. 

32 

28 

85 

11 

5 

28 

2 

Milledgeville, “ 

33 

07 

83 

24 

5 

07 

2.4 

Savannah, “ 

32 

05 

81 

12 

4 

13 

2.7 

Tallahassee, FI. 

30 

26 

84 

27 

5 

03 

1.8 

Pensacola, u 

30 

24 

87 

23 

5 

53 

1.4 

Logansport, Ind. 

40 

45 

86 

22 

5 

24 

2.7 

Cincinnati, O. 

L- 

39 

06 

84 

27 

4 

46 

3.1 




























138 


ELEMENTS OF SURVEYING. [BOOK II. 


METHODS OF ASCERTAINING THE VARIATION. 

14. The best practical method of determining the true 
meridian of a place, is by observing the north star. If this 
star were precisely at the point in which the axis of the 
earth, prolonged, pierces the heavens, then, the intersection 
of the vertical plane passing through it and the place, with 
the surface of the earth, would be the true meridian. But, 
the star being at a distance from the pole, equal to 1° 30' 
nearly, it performs a revolution about the pole in a circle, 
the polar distance of which is 1° 30': the time of revo¬ 
lution is 23 h. and 56 min. 

To the eye of an observer, this star is continually in 
motion, and is due north but twice in 23 h. 56 min.; and 
is then said to be on the meridian. Now, when it departs 
from the meridian, it apparently moves east or west, for 5 
h. and 59 min., and then returns to the meridian again. 
When at its greatest distance from the meridian, east or west, 
it is said to be at its greatest eastern or western elongation. 

The following tables show the times of its greatest 
eastern and western elongations : 

EASTERN ELONGATIONS. 


Days. 

April. 

May. 

J une. 

July. 

August. 

Sept. 


H. 

M. 

H. 

M. 

H. 

M. 

IT. 

M. 

H. 

M. 

H. 

M. 

1 

18 

18 

16 

26 

14 

24 

12 

20 

10 

16 

8 

20 

7 

17 

56 

16 

03 

14 

00 

11 

55 

9 

53 

7 

58 

13 

17 

34 

15 

40 

13 

35 

11 

31 

9 

30 

7 

36 

19 

17 

12 

15 

17 

13 

10 

11 

07 

9 

08 

7 

15 

25 

16 

49 

14 

53 

12 

45 

10 

43 

8 

45 

6 

53 


WESTERN ELONGATIONS. 


Days. 

Oct. 

Nov. 

Dec. 

Jan. 

Feb. 

March. 


H. 

M. 

H. 

M. 

H. 

M. 

H. 

M. 

IT. 

M. 

H. 

M. 

1 

18 

18 

16 

22 

14 

19 

12 

02 

9 

50 

8 

01 

7 

17 

56 

15 

59 

13 

53 

11 

36 

9 

26 

7 

38 

13 

17 

34 

15 

35 

13 

27 

11 

10 

9 

02 

7 

16 

19 

17 

12 

15 

10 

13 

00 

10 

44 

8 

39 

6 

54 

25 

16 

49 

14 

45 

12 

34 

10 

18 

8 

16 

6 

33 

_i 






























SEC. IV.] VARIATION OF THE NEEDLE. 


139 


The eastern elongations are put down from the first 
of April to the first of October; and the western, from the 
first of October to the first of April; the time is computed 
from 12 at noon. The western elongations in the first case, 
and the eastern in the second, occurring in the daytime, 
cannot be used. Some of those put down are also invisi¬ 
ble, occurring in the evening, before it is dark, or after day¬ 
light in the morning. In such case, if it be necessary to de¬ 
termine the meridian at that particular season of the year, 
let 5 h. and 59 min. be added to, or subtracted from, the time 
of greatest eastern or western elongation, and the observ¬ 
ation be made at night, when the star is on the meridian. 

15. The following table exhibits the angle which the me¬ 
ridian plane makes with the vertical plane passing through 
the pole-star, when at its greatest eastern or western elon¬ 
gation : such angle is called the azimuth. The mean angle 
only is put down, being calculated for the first of July of 
each year: 

AZIMUTH TABLE. 


Year. 

Lat. 32° 

Azimuth. 

Lat. 34° 

Azimuth. 

Lat. 36° 

Azimuth. 

Lat. 38° 

Azimuth. 

Lat. 40° 

Azimuth. 

Lat. 42° 

Azimuth. 

Lat. 44° 

Azimuth. 

1851 

1° 45i' 

1° 48' 

1° 502' 

1° 532' 

1° 562' 

2° 002' 

2° 042' 

1852 

1° 45' 

1° 472' 

1° 50' 

1° 53' 

1° 562' 

1° 592' 

2° 032' 

1853 

1° 442' 

1° 47' 

1° 492' 

1° 52J' 

1° 552' 

1° 592' 

2° 032' 

1854 

1° 44 T 

1° 462' 

1° 492' 

1° 52' 

1° 55}' 

1° 59' 

2° 022' 

1855 

1° 43|' 

1° 462' 

1° 48|' 

1° 51f' 

1° 542' 

1° 582' 

2° 02}' 

1856 

1° 43}' 

1° 45 J' 

1° 482' 

1° 512' 

1° 542' 

1° 58' 

2° 012' 

1857 

1° 43' 

1° 45 J' 

1° 48' 

1° 502' 

1° 54' 

1° 57}' 

2° 012' 

1858 

1° 422' 

1° 44f' 

1° 47}' 

1° 50}' 

1° 532' 

1° 57' 

2° 002'! 

I 

1859 

1° 42'' 

1° 44 y 

1° 47' 

1° 492' 

1° 53' 

1° 562' 

to 

o 

o 

o 

1860 

1° 41f' 

1° 44' 

1° 46}' 

1° 492' 

1° 522' 

1° 56' 

2° 00' 

1861 

i 

1° 412' 

1° 432' 

1° 462' 

1° 49' 

1° 52}'j 

1° 55f' 

1° 59J' 

i 


















































































































140 


ELEMENTS OF SURVEYING. [BOOK IL 


The use of the above tables, in finding the true meri¬ 
dian, will soon appear. 

TO FIND THE TRUE MERIDIAN WITH THE THEODOLITE. 

16. Take a board, of about one foot square, paste white 
paper upon it, and perforate it through the centre; the 
diameter of the hole being somewhat larger than the diam¬ 
eter of the telescope of the theodolite. Let this board be 
so fixed to a vertical staff, as to slide up and down freely: 
and let a small piece of board, about three inches square, 
be nailed to the lower edge of it, for the purpose of hold¬ 
ing a candle. 

About twenty-five minutes before the time of the great¬ 
est eastern or western elongation of the pole-star, as shown 
by the tables of elongations, let the theodolite be placed 
at a convenient point and levelled. Let the board be 
placed about one foot in front of the theodolite, a lamp or 
candle placed on the shelf at its lower edge; and let the 
board be slipped up or down, until the pole-star can be 
seen through the hole. The light reflected from the paper 
will show the cross hairs in the telescope of the theodolite. 

Then, let the vertical spider’s line be brought exactly 
upon the pole-star, and, if it is an eastern elongation that 
is to be observed, and the star has not yet reached the 
most easterly point, it will move from the line towards the 
east, and the reverse when the elongation is west. 

At the time the star attains its greatest elongation, it 
will appear to coincide with the vertical spider’s line for 
some time, and then leave it, in the direction contrary to 
its former motion. 

As the star moves towards the point of greatest elonga¬ 
tion, the telescope must be continual^ directed to it, by 
means of the tangent-screw of the vernier plate; and when 
the star has attained its greatest elongation, great, care 
should be taken that the instrument be not afterwards 
moved. 

Now, if it be not convenient to leave the instrument in 
its place until daylight, let a staff, with a candle or small 


SEC. IV.] VARIATION OF THE NEEDLE. 


141 


lamp upon its upper extremity, be arranged at thirty or 
forty yards from the theodolite, and in the same vertical 
plane with the axis of the telescope. This is easily effect¬ 
ed, by revolving the vertical limb about its horizontal axis 
without moving the vernier plate, and aligning the staff to 
coincide with the vertical hair. Then mark the point di¬ 
rectly under the theodolite; the line passing through this 
point and the staff, makes an angle with the true meridian 
equal to the azimuth of the pole-star. 

From the table of azimuths, take the azimuth corres¬ 
ponding to the year and nearest latitude. If the observed 
elongation was east, the true meridian lies on the west of 
the line which has been found, and makes with it an angle 
equal to the azimuth. If the elongation was west, the 
true meridian lies on the east of the line: and, in either 
case, laying off the azimuth angle with the theodolite, gives 
the true meridian. 

TO FIND THE TRUE MERIDIAN WITH THE COMPASS. 

17. 1. Drive two posts firmly into the ground, in a line 

nearly east and west; the uppermost ends, after the posts are 
driven, being about three feet.above the surface, and the 
posts about four feet apart: then lay a plank, or piece of 
timber three or four inches in width, and smooth on the 
upper side, upon the posts, and let it be pinned or nailed, 
to hold it firmly. 

2. Prepare a piece of board four or five inches square, 
and smooth on the under' side. Let one of the compass- 
sights be placed at right angles to the upper surface of the 
board, and let a nail be driven through the board, so that 
it can be tacked to the timber resting on the posts. 

3. At about twelve feet from the stakes, and in the 
' direction of the pole-star, let a plumb be suspended from 

the top of an inclined stake or pole. The top of the pole 
should be of such a height that the pole-star will appear 
about six inches below it; and the plumb should be swung 
in a vessel of water to prevent it from vibrating. 


142 • ELEMENTS OF SURVEYING [BOOK II. 

This being done, about twenty minutes before the time 
of elongation, place the board, to which the compass-sight 
is fastened, on the horizontal plank, and slide it east or 
west, until the aperture of the compass-sight, the plumb- 
line, and the star, are brought into the same range. Then 
if the star depart from the plumb-line, move the compass- 
sight, east or west, along the timber, as the case may be, 
until the star shall attain its greatest elongation, when it 
will continue behind the plumb-line for several minutes; 
and will then recede from it in the direction contrary to 
its motion before it became stationary. Let the compass- 
sight be now fastened to the horizontal plank. During this 
observation it will be necessary to have the plumb-line 
lighted: this may be done by an assistant holding a candle 
near it. 

Let now a staff, with a candle or lamp upon it, be 
placed at a distance of thirty or forty yards from the 
plumb-line, and in the same direction with it and the com¬ 
pass-sight. The line so determined, makes, with the true 
meridian, an angle equal to the azimuth of the pole-star; 
and, from this line, the variation of the needle is readily 
determined, even without tracing the true meridian on the 
ground. 

Place the compass upon this line, turn the sights in the 
direction of it, and note the angle shown by the needle. 
Now, if the elongation, at the time of observation, was 
west, and the north end of the needle is on the west side of 
the line, the azimuth, plus the angle shown by the needle, 
is the true variation. But should the north end of the 
needle be found on the east side of the line, the elonga¬ 
tion being west, the difference between the azimuth and 
the angle would show the variation: and the reverse when 
the elongation is east. 

1. Elongation west, azimuth . . 2° 04' 

North end of the needle on the west, angle 4° 06' 


Yariation 6° 10' west. 




X 


SEC. IV.] VARIATION OF THE NEEDLE. 143 

2. Elongation west, azimuth . . 1° 59' 

North end of the needle on the east, angle 4° 50' 

Yariation 2° 51' east. 

3. Elongation east, azimuth . . 2° 05' 

North end of the needle on the west, angle 8° 30' 

Yariation 6° 25' west. 

4. Elongation east, azimuth . . 1° 57' 

North end of the needle on the east, angle 8° 40' 

Yariation 10° 37' east. 


Remark I. The yariation at West Point, in Septem¬ 
ber, 1835, was 6° 32' west. 

Remark II. The variation of the needle should al¬ 
ways be noted on every survey made with the compass, 
and then if the land be surveyed at a future time, the old 
lines can always be re-run. 

18. It has been found by observation, that heat and 
cold sensibly affect the magnetic needle, and that the same 
needle will, at the same place, indicate different lines at 
different hours of the day. . 

If the magnetic meridian be observed early in the 
morning, and again at different hours of the day, it will 
be found that the needle will continue to recede from the 
meridian as the day advances, until about the time of the 
highest temperature, when it will begin to return, and at 
evening will make the same line as in the morning. This 
change is called the diurnal variation , and varies, during 
the summer season, from one-fourth to one-fifth of a 
degree. 

19. A very near approximation to a true meridian, and 
consequently to the variation, may be had, by remember¬ 
ing that the pole-star very nearly reaches the true meri¬ 
dian, when it is in the same vertical plane with the star 
Alioth in the tail of the Great Bear, which lies nearest the 
four stars forming the quadrilateral. 








144 


ELEMENTS OF SURVEYING. [BOOK IL 


The vertical position can be ascer¬ 
tained by means of a plumb-line. To 
see the spider’s lines in the field of the 
telescope at the same time with the 
star, a faint light should be placed 
near the object-glass. When the 
plumb-line, the star Alioth, and the 
north star, fall on the vertical spider’s 
line, the horizontal limb is firmly 
clamped, and the telescope brought 
down to the horizon ; a light, seen 
through a small aperture in a board, 
and held at some distance by an as¬ 
sistant, is then moved according to signals, until it is cov¬ 
ered by the intersection of the spider’s lines. A picket 
driven into the ground, under the light, serves to mark the 
meridian line for reference by day, when the angle formed 
by it and the magnetic meridian may be measured. 


I 

i 

i 


<> 


\ 


BOOK III. 

LEVELLING AND TOPOGRAPHICAL SURVEYING. 



SECTION I. 

OF LEVELLING. 

T // 

. L 

1. Levelling is the art of determining the relative dis¬ 
tances of points from the centre of the earth. 

2. A line whose points are all equally distant from the 
centre of the earth, is called a line of true level , and a sur¬ 
face, all whose points are equally distant from the centre 
of the earth, as the surface of still water, is called a level 
surface. 

3. One point is said to be above another, when it is 
farther from the centre of the earth; and this difference of 
distance from the centre, is called the difference of level be¬ 
tween the two points. 

4. A straight line drawn tangent to a line of true level 
at any point, is a horizontal line, and is called a line of 
apparent level. Thus (PL 4, Fig. 1), if C is the centre of 
the earth and AEF a line of true level, ABB is a line of 
apparent level. This is the line of level determined by an 
instrument. The difference between the apparent and true 
level at any distant station B , as determined from A, is BE\ 
or the excess of the secant of the arc AE over the radius. 

5. To find a general formula for computing this excess, 
we have (Geom. B. IY., Prop. XXX.) 

ZB 2 = BE {BE + 2EC ); 

but since the arc AE is very small in comparison with the, 

10 • 




146 


ELEMENTS OF SURVEYING. [BOOK III 


radius of the earth, the arc AE will not differ sensibly from 
the tangent AB; the diameter 2EG may, for the same 
reason, be taken for the secant (.BE + 2EG) : hence, 

AE 2 = BE X 2EG, or dividing by 2EG, 


BE = 


AE 2 
2EG 



If we take the mean diameter of the earth to be 7919 

AE 1 

miles, formula (1) gives BE= (2) : hence, 

The departure of the apparent from the true level , starting 
from a given point, is equal to the square of the distance to the 
second point , divided by the diameter of the earth. 

If in formula (2) you give to AE , in succession, every 
value from 1 chain to any given number of chains, (say 
100), and reduce at the same time both terms of the frac¬ 
tion to inches, a table may be computed as below. 


Table showing the differences in inches between the true and ap¬ 
parent level , for distances between 1 and 100 chains. 


Chains. 

Inches. 

Chains. 

Inches. 

Chains. 

Inches. 

Chains. 

Inches. 

1 

.001 

26 

.845 

51 

3.255 

76 

7.221 

2 

.005 

27 

.911 

52 

3.380 

77 

7.412 

3 

.011 

28 

.981 

53 

3.511 

78 

7.605 

4 

.020 

29 

1.051 

54 

3.645 

79 

7.802 

. 5 

.031 

30 

1.125 

55 

3.781 

80 

8.001 

6 

.045 

31 

1.201 

56 

3.925 

81 

8.202 

7 

.061 

32 

1.280 

57 

4.061 

82 

8.406 

8 

.080 

33 

1.360 

58 

4.205 

83 

8.612 

9 

.101 

34 

1.446 

59 

4.351 

84 

8.832 

10 

.125 

35 

1.531 

60 

4.500 

85 

9.042 

11 

.151 

36 

1.620 

61 

4.654 

86 

9.246 

12 

.180 

37 

1.711 

62 

4.805 

87 

9.462 

13 

.211 

38 

1.805 

63 

4.968 

88 

9.681 

14 

.245 

39 

1.901 

64 

5.120 

89 

9.902 

15 

.281 

40 

2.003 

65 

5.281 

90 

10.126 

16 

.320 

41 

2.101 

66 

5.443 

91 

10.351 

17 

.361 

42 

2.208 

67 

5.612 

92 

10.587 

18 

.405 

43 

2.311 

68 

5.787 

93 

10.812 

19 

.451 

44 

2.420 

69 

5.955 

94 

11.046 

20 

.500 

45 

2.531 

70 

6.125 

95 

11.233 

21 

.552 

46 

2.646 

71 

6.302 

96 

11.521 

22 

.605 

47 

2.761 

72 

6.480 

97 

11.763 

23 

.661 

48 

2.880 

73 

6.662 

98 

12.017 

24 

.720 

49 

3.004 

74 

6.846 

99 

12.246 

25 

.781 

50 

3.125 

75 

7.032 

100 

12.502 
























THE Y LEVEL. 


147 


SEC. I.] 

* 

Observing that for AE= 80 chains = 1 mile, BE is equal 
to 8.001 inches, or about two-thirds of a foot, and since 
the differences of level vary as the squares of the dis¬ 
tances, we have the following easy rule for finding the cor¬ 
rection in feet. 

The correction for curvature , in feet , is equal to two-third, 
of the square of the distance in miles. 

INSTRUMENTS. 

6. Before proceeding further in the discussion of the 
principles of levelling, we will describe some of the in¬ 
struments used, and first, 

THE Y LEVEL. 

7. A level is an instrument used to determine horizontal 
lines, and the difference of level of any two -points on the 
surface of the earth. 

The part of the instrument shown in PI. 4, Fig. 2, rests 
on a tripod, to which it is permanently attached at Z. HH 
is a horizontal brass plate, through which four levelling 
screws with milled heads are passed, and worked against a 
second horizontal plate GG. Two of these screws, K and 
f are seen in the figure. S. is a clamp-screw, which, being 
loosened, allows the upper part of the instrument to turn 
freely around its axis. Q is a tangent-screw, by means of 
which the upper part of the instrument is moved gently, 
after the clamp-screw S has been made fast. EE is a hori¬ 
zontal bar, perpendicular to which are the wyes, designat¬ 
ed Y’s, that support the telescope LB. This telescope is 
confined in the Y’s by the loops r, r, which are fastened 
by the pins p and p. The object-glass B , is adjusted to 
its focus by the screw AT, the eye-glass L slides out and 
in freely. The screws f f work the slide which carries 
the horizontal hair; and two horizontal screws, only one 
of which, a, is seen, work the slide that carries the verti¬ 
cal hair. CD is an attached spirit-level. The screw N 
elevates and depresses the Y, nearest the eye-glass. In 
some instruments this Y is elevated and depressed, by 
means of two screws at M and R. 


148 


ELEMENTS OF SURVEYING. [BOOK III. 


Before using this level, it must be adjusted. The ad¬ 
justment consists in bringing the different parts to their 
proper places. 

The line of collimation is the axis of the telescope. With 
this axis, the line drawn through the centre of the eye¬ 
glass and the intersection of the spider’s lines, within the 
barrel of the telescope, ought to coincide. 

First adjustment.* To fix the intersection of the spider’s 
lines in the axis of the telescope. 

Having screwed the tripod to the instrument, extend 
the legs, and place them firmly. Then loosen the clamp- 
screw S, and direct the telescope to a small, well-defined, 
and distant object. Then slide the eye-glass till the spider’s 
lines are seen distinctly; after which, with the screw W, 
adjust the object-glass to its proper focus, when the object 
and the spider’s lines will be distinctly seen. Note now 
the precise point covered by the intersection of the spider’s 
lines. 

Having done this, revolve the telescope in the Y’s, half 
round, when the attached level CD will come to the upper 
side. See if, in this position, the horizontal hair appears 
above or below the point, and in either case, loosen the 
one, and tighten the other, of the two screws which work 
the horizontal hair, until it has been carried over half the 
space between its last position and the observed point. 
Carry the telescope back to its place; direct again, by the 
screws at M and A, the intersection of the spider’s lines to 
the point, and repeat the operation, till the horizontal hair 
neither ascends nor descends while the telescope is revolv¬ 
ed. A similar process will arrange the vertical hair, and 
the line of collimation is then adjusted. 

Second adjustment. To make the axis of the attached 
level CD parallel to the line of collimation. 

Turn the levelling screws M and R ) until the bubble 


* This, and some of the following adjustments, are so similar to those of the 
theodolite, that they would not be here repeated, but that some may use the 
level without wishing to study a more complicated instrument. 



SEC I.] 


THE Y LEVER. 


149 


of the level DO stands at the middle of the tube. Then 
open the loops, and reverse the telescope. If the bubble 
still stands at the middle of the tube, the axis of the level 
is horizontal; but if not, it is inclined, the bubble being 
at the elevated end. In such case, raise the depressed, or 
depress the elevated end, by means of the small screw h, 
half the inclination ; and then with the screws, at M and R, 
bring the level to a horizontal position. Reverse the teles¬ 
cope in the Y’s, and make similar corrections again; and 
proceed thus, until the bubble stands in the middle of 
the tube, in both positions of the telescope; the axis of the 
level is then horizontal. 

f 

Let the telescope be now revolved in the Y’s. If the 
bubble continues in the middle of the tube, the axis of the 
level is not only horizontal, but also parallel to the line of 
collimation. If, however, the bubble recedes from the centre, 
the axis of the level is inclined to the line of collimation, 
and must be made parallel to it, by means of two small 
screws, which work horizontally; one of these screws is 
seen at q. By loosening one of them, and tightening the 
other, the level is soon brought parallel to the line of col¬ 
limation ; and then, if the telescope be revolved in the Y’s, 
the bubble will continue at the. middle of the point of the 
tube. It is, however, difficult to make the first part of this 
adjustment, while the axis of the level is considerably in¬ 
clined to the line of collimation: for, allowing the level to 
be truly horizontal in one position of the telescope, after it 
is reversed, there will be but one corresponding position 
in which the bubble will stand at the middle of the tube. 
This suggests the necessity of making the first part of the 
adjustment with tolerable accuracy; then, having made the . 
• second with care, re-examine the first, and proceed thus 
till the adjustment is completed. 

Third adjustment. To mahe the level CD and the 
line of collimation perpendicular to the axis of the instrument, 
or p>arallel to the horizontal bar EE. 

Loosen the clamp-screw S.\ and turn the bar EE\ until 
the level DO comes directly over two of the levelling 


150 


ELEMENTS OF SURVEYING. [BOOK IIL 


screws. By means of these screws, make the level CD 
truly horizontal. Then, turn, the level quite round; if, 
during the revolution, it continue horizontal, it must be at 
right angles to the axis of the instrument about which it 
has been revolved. But if, after the revolution, the level 
CD be not horizontal, rectify half the error with the screws 
at M and R, and half with the levelling screws. Then 
place the bar EE over the other two levelling screws, and 
make the same examinations and corrections as before; and 
proceed thus, until the level can be turned entirely around 
without displacing the bubble at the centre. When this 
can be done, it is obvious that the level DC and the line 
of collimation, are at right angles to the axis of the* instru¬ 
ment about which they revolve; and since the axis is care¬ 
fully adjusted by the maker, at right angles to the bar EE, 
it follows, that the line of collimation, the level DC, and 
the bar EE, are parallel to each other. 

The level is now adjusted. When used, however, it is 
best to re-examine it every day or two, as the work will 
be erroneous unless the instrument is accurately adjusted. 

THE WATER LEVEL. 

8. The Water Level is an instrument that possesses the 
advantage of never * requiring adjustment, and also of being 
very cheap; in fact, any ordinary workman may con¬ 
struct one. Having no telescope, it is impossible to take 
long sights, but for such work as is required to be done 
by the ordinary surveyor, it gives very good results. 

Two brass cups, C and D, about one inch in diam¬ 
eter, and from four to five inches in height, are permanent¬ 
ly attached to a hollow brass tube of three feet long and 
half an inch in di- QE 
ameter. The cups 
are for the purpose A L- 
of receiving the 
ends E and F of 
two bottles, the 
bottoms of which have been cut off. The bottoms may be 
cut off by means of a hot iron, or file. The ends are fixed 
in their places with putty. 


















SEC. 1] 


LEVELLING STAVES. 


151 


The projecting axis g works in a hollow cylinder h , 
which forms the top of a stand. The tube, when the level 
is required for use, is filled with water (colored with lake 
or indigo), till it nearly reaches the necks of the bottles. 
After placing the stand tolerably level by the eye, with¬ 
draw both corks, and the surface of the water in the bot¬ 
tles will indicate a horizontal line in whatever direction the 
tube is turned. This level is well adapted to tracing con¬ 
tour lines as described in the next section. 


LEVELLING STAVES. 

9. The levelling staves are used to determine the points 
at which a given horizontal line intersects lines that are 
perpendicular to the surface of the earth, and to show the 
distances of such points of intersection from the ground. 

The levelling staff is a necessary accompaniment to 
either of the levels described. Several kinds are used. 

One of the best, consists of a staff 12 or 15 feet long, 
and graduated to feet, tenths, and hundredths. A sliding 
vane is made to move up or down by a 
cord and pulleys, and on the vane is a 
vernier, by means of which the reading 
of the staff may be effected .to thou¬ 
sandths of a foot. AB represents a 

portion of the staff, DC the moveable 
vane, with an opening EF\ through which 
the graduation on the staff is seen. F is 
the vernier of the vane, the 0 being de¬ 
termined by the transverse line DC. To 
render this line more distinct, the vane 
is divided into four quarters, and the 
alternate ones are painted black, which, 
by their contrast with the white quar¬ 
ters, show the line DC distinctly. 

10. Another variety of levelling staff is shown in PI. 4, 
Fig. 8. It is formed of two pieces, each about six feet 
long, one of which slides in a groove of the other, and 
bears a vane similar to that already described. It is grad¬ 
uated to feet, inches, and eighths of an inch. The line of 



















152 


ELEMENTS OF SURVEYING. [BOOK III- 


sight of tlie telescope is always directed to the centre of 
the vane. When the line of sight is less than six feet from 
the ground, the staff is reversed,—the vane run up the staff, 
and the readings made by means of the reversed figures at the 
right, where they are cut by the lower line of the vane. 
When the line of sight is more than six feet from the ground, 
the staff stands as in the figure, the reading is then made at 
the line be, and the figures indicating'the height, are found on 
the sliding part which carries the vane. The reading of the 
staff, as it now stands, is seven feet. 

11. Another rod is sometimes used on which the figures 
are marked so plainly, that they may be read by the ob¬ 
server himself, without the aid of a vane; thus avoiding 
errors through ignorance or negligence of the rodman. 

If the telescope used, inverts the object, the figures should 
be made inverted on the staff, so as to appear erect. Each 
of the rods described, has its advantages, and either one may 
be used according to the circumstances of the survey. 

12. There is a method of testing the adjustments of the 
Y level, which ought not to be neglected, since all the re¬ 
sults depend on the accuracy of the instrument. The 
method is this: 

The level being adjusted, place it at any convenient 
point, as G (Fig. 4). At equal distances of about 100 yards, 
on either side, and in the same line with the level, place 
the levelling staves, CE, BF. Make the level horizontal 
with the levelling screws. Then, turn it towards either 
staff, as BF, and run the vane up or down, as required, 
until the intersection of the hairs strikes the centre : then 
make the slide fast, and note carefully the height of the 
vane. Turn the level half round, and do the same in 
respect of the staff CF. 

Let the telescope be now reversed in the Y’s. Sight 
again to the staff BF, and note the exact height of the 
vane. Let the telescope be now turned half round, and 
the same be done for the staff CE. If the two heights 
last observed, are equal to those first noted, each to each, 
the line of collimation is perpendicular to the axis of the 


SEC. I.] 


OF LEVELLING. 


153 


instrument, and if the bubble lias, at the same time, pre¬ 
served its place at the middle point of the tube, the instru¬ 
ment is truly adjusted. 

For, had the line of collimation been inclined to the 
axis of the level, it would, in the first instance, have taken 
the direction AF or Ad ; and when turned half round, it 
would have taken the direction AE or Ab. The telescope 
being reversed in the Y’s, and again directed to the staff 
BF\ the line of collimation would take the direction Ad or 
AF 1 and when turned to the staff CE\ it would take the 
direction Ab or AE: and the two distances BF\ Bd , or Cb, 
CE\ can only be equal to each other when the line of col¬ 
limation falls on the horizontal line cgf 

LEVELLING IN THE FIELD. _ 

13. The operation of levelling may be undertaken: 

1st. For the purpose of determining the difference of 
level between two given points. 

2d. For the purpose of obtaining a section or profile 
along a given line, as in the . reconnoissance for a line of 
railroad. 

3d. For the purpose of determining the contour lines in 
a topographical survey, as described in the next section. 

DIFFERENCE OF LEVEL BETWEEN TWO POINTS. 

14. When it is proposed to find the difference of level 
of any two objects, or stations, all levels made in the di¬ 
rection of the station at which the work is begun, are 
called, for the sake of distinction merely, bach-siglits; and 
levels taken in the direction of the other station, fore¬ 
sights. 

Before going on the field with the level, rule three 
columns, as below, and head them, stations, back-sights, 
fore-sights. 


154 


ELEMENTS OF SURVEYING. [BOOK III. 


FIELD NOTES. 


Stations. 

Back-Sights. 

— Fore-Sights. 

1 

10 

3 

2 

11-6 

0 

8 

6-8 

4-9 

4 

8-9 

8-8 

Sums . . 

. . . 81-11 

16-0 


16-00 


Dif. of level. 

. . . 15-11 



EXAMPLE. 

Find the difference of level between any two points , as A and 

G (PI. 4, Fig. 5.) 

The level being adjusted, place it at any point, as B , as 
nearly in the line joining A and G as may be convenient. 
Place a levelling staff at M, and another at N, a point 
lying as near as may be in the direction of G. Make the 
level horizontal, by means of the levelling screws; turn the 
telescope to the staff at A, and direct the person at the 
staff to slide up the vane until the horizontal line ah pierces 
its centre; then note the distance Ab (equal to 10 feet in 
the present example), and enter it in the column of back¬ 
sights, opposite station 1. Sight also to the staff at iVJ and 
enter the distance Na, equal to 8 feet, in the column of fore¬ 
sights, opposite station 1. 

Take up the level, and place it at some other convenient 
station, as C,\ and remove the staff at M, to M. Having 
levelled the instrument, sight to the staff at N, and enter 
the distance Nd, 11 feet 6 inches, in the column of back¬ 
sights, opposite station 2 : sight also to the staff at M, and 
enter the distance Mf equal 0, in the column of fore-sights, 
opposite station 2. 












SEC. I] 


OF LEVELLING. 


155 


Let the level be now removed to any other station, as 
D, and the staff at iVJ to some other point, as P. Let the 
distance Mg, equal to 6 feet 8 inches, be entered in the 
column of back-sights, opposite station 8, and the distance 
Pli , equal to 4 feet 9 inches, in the column of fore-sights. 
Let the instrument be now placed at E\ and the distance 
Pm, equal to 3 feet 9 inches, and Gn, equal to 8 feet 3 
inches, be entered opposite station 4, in their proper 
columns. 

It is evident from the figure, that the difference of level 
NF, between A and N, is equal to the back-sight bA, dim¬ 
inished by the fore-sight aiV; also that the difference of 
level between E and M is equal to the back-sight dE, dim¬ 
inished by the foresight 0, and since each set of obser¬ 
vations is entirely independent of every other set, we may 
infer that the difference of level between two points as determin¬ 
ed by one position of the level, is equal to the back-sight, dim¬ 
inished by the fore-sight. If the fore-sight be greater than the 
back-sight, the difference will be affected with a minus sign, 
a result which shows that the second point is lower than 
the first. Generally, the difference of level between any two 
points, determined as above, is equal to the sum of the back¬ 
sights diminished by the sum of the fore-sights. If the result is 
plus, the second point is higher than the first; if negative, 
it is lower. 

In the example given, the difference of level between 
A and 6r, is 15 feet 11 inches. 

i 

15. In the previous example, we did not regard the dif¬ 
ference between the true and apparent level. If it be ne¬ 
cessary to ascertain the result with extreme accuracy, this 
difference must be considered: and then, the horizontal 
distances between the level, at each of its positions, and the 
staves, must be measured, and the apparent levels dimin¬ 
ished by the differences of level; which differences can be 
found from the table. 


156 


ELEMENTS OF SURVEYING. [BOOK III 


THE FOLLOWING IS SUCH AN EXAMPLE. 


Stat. 

Back-sts. 

Distances. 

Fore-st. 

Distances. 

r 

Cor.back-sights 

Cor. fore-sts. 

1 

9-8 

20 ch. 

1-6 

32 ch. 

9-7.500 

1-4.720 

2 

8-7 

25 ch. 

2-4 

28 ch. 

8-6.219 

2-3.019 

3 

5-2 

18 ch. 

3-1 

16 ch. 

5-1.595 

8-0.680 

4 

10-3 

29 ch. 

1-9 

87 ch. 

10-1.949 

0-11.538 

5 

11-0 

45 ch. 

2-5 

72 ch. 

10-9.469 

1-10.520 


44-2.782 

9-6.477 


In this example, the first column shows the stations; 
the second, the hack-sights; the third, the distances from 
the level in each of its positions to the hack staff; the 
fourth, the fore-sights; the fifth, the distances from the 
level to the forward staff; the sixth and seventh, are the 
columns of back and fore-sights, corrected by the difference 
of level. The corrections are thus made:—The difference 
of level in the table corresponding to 20 chains, is 5 tenths 
of an inch, which being subtracted from 9 feet 8 inches, 
leaves 9 feet 7.5 inches for the corrected back-sights; this 
is entered opposite station 1 in the sixth column. The dif¬ 
ference of level corresponding to 32 chains, is 1.280 inches, 
which being subtracted from the apparent level, 1 foot 6 
inches, leaves 1 foot 4.720 inches for the true fore-sight 
from station 1. The other corrections are made in the 
same manner. 

The sum of the back-sights being 44 feet 2.732 inches, 
and the sum of the fore-sights 9 feet 6.477 inches, it fol¬ 
lows, that the difference, 34 feet 8.255 inches, is the true 
difference of level. 

16. In finding the true from the apparent level, we 
have not regarded the effect caused by refraction on the 
apparent elevation of objects, as well because the refraction 
is different in different states of the atmosphere, as because 
the corrections are inconsiderable in themselves. 

17. The small errors that would arise from regarding 
the apparent as the true level, may be avoided by ytlaciny 



















SEC. I.] 


OF LEVELLING. 


157 


the levelling staves at equal distances from the level. In sucli 
case, it is plain, 1st, that equal corrections must be made 
in the fore and back-sights; and, 2dly, that when the fore 
and back-sights are diminished equally, the result, which is 
always the difference of their sums, will not be affected. 

This method should always be followed, if practicable, 
as it avoids the trouble of making corrections for the dif¬ 
ference of true and apparent level. 

The differences between the true and apparent level, 
being very inconsiderable for short distances, if only ordi¬ 
nary accuracy be required, it will be unnecessary to make 
measurements at all. Care, however, ought to be taken, 
in placing the levelling staves, to have them at as nearly 
equal distances from the level as can be determined by the 
eye; and if the distances are unequal, let the next distances 
also be made unequal; that is, if the back-sight is^the 
longer in the first case, let it be made proportionably 
shorter in the second, and the reverse. 

LEVELLING FOR SECTION. 

18. Having decided upon the line along which a section 
is to be taken, let a permanent mark be made at the be¬ 
ginning of the line: this is called a bench-mark. A bench¬ 
mark is made by drilling a hole in a rock, or by painting 
upon a rock or fence, or sometimes by driving a stake in 
the ground, with its upper end marked by a nail-head. 
Bench-marks should be made from time to time along the 
line, to serve as checks, in case a re-survey should become 
necessary. 

The operations in the field are similar to those in the 
last example, and the field notes are kept in the same 
manner, except that a new column is added for bearings, 
when it is necessary to make a plot of the line of survey. 
The total distance of each point above or below the start¬ 
ing point may be computed, and written in a separate col¬ 
umn, paying particular attention to the signs. We annex 
an example, in which the heights are estimated in feet, 
and decimals of a foot. 


ELEMENTS OF SURVEYING. [BOOK IIL 


158 


Sta¬ 

tion. 

Distances in 

feet. 

B. Sight. 

F. Sight. 

Dif. between 

B. S. and F. S. 

Total Dif. of 
Level. 

REMARKS. 

1 

650 

2.35 

14.55 

-12.20 

— 

12.20 

Commenced at bench-mark A. 

2 

700 

3.56 

9.58 

- 6.02 

— 

18.22 


3 

750 

10.34 

6.21 

+ 4.13 

— 

14.09 


4 

650 

14.55 

0.25 

+14.30 

+ 

0.21 


5 

600 

9.98 

1.67 

+ 8.31 


8.52 


6 

650 

3.62 

14.54 

-10.92 

— 

2.40 



B.M 

1.23 

13.45 

-12.22 

— 

14.62 

Bench-mark on rock. 

7 

500 

2.23 

12.05 

- 9.82 

— 

24.44 

Terminating at.fi.2f on oak tree. 

• 

8 

750 

6.20 

19.55 

-13.35 

— 

37.79 

• 


The fifth column shows the difference of level between 
any two consecutive positions of the levelling staff, and is 
found by subtracting the fore-sight from the corresponding 
back-sight, and giving to the remainder the proper sign. 
The sixth column shows the distance of each point above 
or below the bench-mark A , and is obtained by continual 
additions of the numbers in column 5. Thus, 

(- 12.20) + (- 6.02) = - 18.22; (- 18.22) + 4.13 - -14.09; 
and so on. 

It will be seen that the point of termination is 37.79 
feet below the starting point. 

PLOTTING THE SECTION OR PROFILE. 

19. The vertical distances being generally very small as 
compared with the horizontal distances, two different scales 
become necessary in plotting a profile. In order that the 
vertical distances may be fully exhibited in the plan, the 
scale used for them is much larger than is used for lines 
measured in a horizontal direction. This becomes absolutely 
necessary where long lines of profile, with a gentle slope, 
are to be plotted, as is always the case in the trial section 
of a railroad survey. We shall illustrate the manner of 
plotting, by drawing the section determined by the field- 
notes just given. 

20. Draw a horizontal line AK, called a datum line, and 

















SEC. II.] TOPOGRAPHICAL SURVEYING. 


159 


assume some point as A, to represent the point of begin¬ 
ning : lay off on the datum line, distances equal to the 

L 



measured distances 650, 700, 750, &c., feet to K, using in 
this case a scale of 1500 feet to 1 inch. At the points B , 
0\ D , A, &c., thus determined, erect perpendiculars, making 
them equal, on a scale of 25 feet to the inch, to the cor¬ 
responding differences of level taken from the field-book; 
through the points thus found, draw the irregular line 
APLM } and it will represent the surface of the ground 
along the line of level. 

The bench-mark, between stations 7 and 8, is not plotted, 
as it is supposed to be out of the line of the section, and 
no distances are measured to it. 


SECTION II. 

TOPOGRAPHICAL SURVEYING. 

21. Besides the surveys that are made to determine the 
area of land and the relative positions of objects, it is fre¬ 
quently necessary to make minute and careful examinations 
for the purpose of ascertaining the form and accidents of 
the ground, and to make such a plan as will distinguish 
the swelling hill from the sunken valley, and the course 
of the rivulet from the unbroken plain. 










160 


ELEMENTS OF SURVEYING. [BOOK IIL 


22. This branch of surveying is called Topography. In 
surveys made with a view to the location of extensive 
works, the determination of the slopes and irregularities of 
the ground is of the first importance: indeed, the examina¬ 
tions would otherwise be useless. 

23. The manner of ascertaining these irregularities is, to 
suppose the surface of the ground to be intersected by a 
system of horizontal planes at equal distances from each 
other; the curves determined by these secant planes, being 
lines of the surface, will indicate its form at the places of 
section, and, as the planes are nearer or more distant from 
each other, the form of the surface is more or less accu¬ 
rately ascertained. 

If such a system of curves be determined, and then pro¬ 
jected or let fall on a horizontal plane, it is obvious that 
the curves on such plane will be nearer together or farther 
apart, as the ascent of the hill is steep or gentle. 

If, therefore, such intersections be made, and the curves 
so determined be accurately delineated on paper, the map 
will give such a representation of the ground as will 
show its form, its inequalities, and its striking character¬ 
istics. 

24. The subject divides itself, naturally, into two parts. 

1st. To make the necessary examinations and measure¬ 
ments on the field; and, 

* 2d. To make the delineations on paper. 

For the former of these objects, the theodolite is the 
best instrument; the common level, however, will answer 
all the purposes, though it is less convenient. 

Before going on the field, it is necessary to provide a 
number of wooden stakes, about two feet in length, with 
heads. These stakes are used to designate particular points, 
and are to be driven to the surface of the ground. A 
nail should then be driven into the head of each of them, 
to mark its centre. 

25. We shall, perhaps, be best understood, by giving an 
example or two, and then adding such general remarks as 


161 


SEC. II] TOPOGRAPHICAL SURVEYING. 

will extend the particular cases to all others that can 
occur. 

Let A (PI. 4, Fig. 6), be the summit of a hill, the con¬ 
tour of which it is required to represent. At A, let a 
stake be driven, and let the axis of the theodolite, or level, 
be placed directly over the nail which marks its centre. 
From A, measure any line down the hill, as AB , using the 
telescope of the theodolite or level to arrange all its points 
in the same vertical plane. Great care must be taken to 
keep the measuring chain horizontal, for it is the horizontal 
distances that are required. At different points of this line, 
as a, b , c, d , &c., let stakes be driven, and let the horizon¬ 
tal distances Aa, ab, be, and cd, be carefully measured. In 
placing the stakes, reference must be had to the abruptness 
of the declivity, and the accuracy with which the surface 
is to be delineated: their differences of level ought not to 
exceed once and a half, or twice, the distance between the 
horizontal planes of section. 

Having placed stakes, and measured all the distances 
along the lirie AB, run another line down the hill, as AC [ 
placing stakes at the points e, f g, and h, and measuring 
the horizontal distances Ae, ef, fg, and gh. Kun also the 
line AD , placing stakes at i, l, m, and n , and measuring 
the horizontal distances Ai, il, Im, and mn. 

Each line, AB, A C, AD, running down the hill from A, 
may be regarded as the intersection of the hill by a verti- 
.cal plane; and these secant planes are to be continued over 
all the ground which is to be surveyed. If the work is 
done with a theodolite, or with a level having a compass, 
the angles DAB and BAC, contained by the vertical se¬ 
cant planes, can be measured; if it is done with a level, 
having no needle, let any of the distances ae, bf, ai, bl, &c., 
be measured with the chain, and there will then be known 
the three sides of the triangles Aae, Abf, Aai, Abl, &c. 

Let now, the difference of level of the several points 
marked in each of the lines AB, AD, AC, be determined. 

In the present example the results of the measurements 
and levelling, are— 


11 


162 


ELEMENTS OF 
Line 

Distances. 

Aa — 40 feet 
ab = 50 “ 

be = 30 “ 
cd *= 46 “ 

Line 

Distances. 

Ae = 28 feet 
ef = 45 “ 

fg = 55 “ 

gh =49 “ 

Line 

Distances. 

Ai = 25 feet 
il = 55 “ 

Im =38 “ 
mn — 48 “ 

Angle (7Ai? = 25°, 


SURVEYING. [BOOK III 

# 

AB. 

Difference of Level. 

A above a 12 feet 
a above b 8 u 
b above c 9 “ 

c above d 11 “ 

A<7. 

Difference of Level. 

A above e 11 feet 
e above / 9 “ 

/ above g 12 “ 

<7 above A 14 “ 

AZ>. 

Difference of Level. 

A above i 9 feet 
i above l 13 “ 

l above m 7 “ 

m above n ^.4 “ 

Angle DAB = 30°. 


These data are sufficient, not only to find the intersec¬ 
tions of horizontal planes with the surface of the hill, but 
also for delineating such curves of section on paper. 

Having drawn on the paper the line AB , lay off the 
angle BAC =25°, and the angle BAD — 30°. Then, from 
a convenient scale of equal parts, lay off the distances Aa, 
ab, be, cd, Ae, ef, fg, gh, Ai, il, Im, and mn. 

Let it be required that the horizontal planes be at a 
distance of eight feet from each other. Since A is the 
highest point of the hill, and the difference of level of the 
points A and a, is 12 feet, the first plane, reckoning down¬ 
wards, will intersect the line traced on the ground from A 
to B, between A and a. Regarding the descent as uniform, 
which we may do for small distances without sensible error, 
we have this proportion; as the difference of level of the 
points A and a, is to the horizontal distance Aa, so is 8 
feet, to the horizontal distance from A to where the first 





163 


SEC. II] TOPOGRAPHICAL SURVEYING. 

• 

horizontal plane will cut the line from A to B. This dis¬ 
tance being thus found, and laid off from A to <?, gives o, 
a point of the curve in which the first plane^intersects the 
ground. The points at which it cuts the line from A to (7, 
and the line from A to D , are determined similarly, and 
three points in the first .curve are thus found. 

The graphic operations are greatly facilitated by the aid 
of the sector. Let it be borne in mind, that the descent 
from A to a, is 12 feet, and that it is required, upon the 
supposition of the descent being uniform, to find that part 
of the distance corresponding to a descent of 8 feet. Take 
the distance from A to a, in the dividers, and open the 
arms of the sector until the dividers will reach from 12 on 
the line of equal parts, on one side, to 12 on the line of 
equal parts, on the other. Then, without changing the 
angle, extend the dividers from 8 on one sid£, to 8 on the 
other; this will give the proportional distance to be laid 
off from A to o. Or, if the dividers be extended from 4 
to 4, the proportional distance may be laid off from a 
to o. 

If the distances to be taken from the sector fall too 
near the joint, let multiples of them be used ; as for in¬ 
stance, on the French sectors,' let the arms be extended 
until the dividers reach from 120 on the one, to 120 on 
the other, then 80 or 40 will be the proportional numbers. 
Other multiples may be used, though it is generally more 
convenient’ to multiply by 10. 

26. The second plane is to pass 8 feet below the first, 
that is, 16 feet below A, or 4 feet below a, a being 12 feet 
below A. Take the distance ab in the dividers, and ex¬ 
tend the sector, so that the dividers will reach from 8 to 
(the descent from a to b being 8 feet) 8, or from 80 to 
80; then, the distance from 4 to 4, or from 40 to 40, being 
laid off from a to y>, gives y>, a point of the second curve. 

The difference of level between a and b being 8 feet, 
and the difference of level between a and p being 4 feet, 
the difference of level 'between p and b must also be 4 
feet; hence, the third plane will pass 4 feet below b, and 


164 


ELEMENTS OF SURVEYING. [BOOK III. 


g, determined as above, is a point of the third curve, and 
so on. After having determined the points in which each 
contour line cuts the lines diverging from A, let the con¬ 
tour lines be drawn through them, so as to indicate the 
surface of the hill. The numbers (8), (16), &c., show the 
vertical distances of the respective planes below the point A. 


27. Having drawn the horizontal curves, the next thing 
to be done is so to shade the drawing that it may represent 
accurately the surface of the ground. This is done by 
drawing a system of small broken lines, as in the figure, 
perpendicular in direction to the horizontal curves already 
described. In all topographical representations of undulat¬ 
ing ground, the lines of shading are drawn perpendicular to 
the horizontal curves. 


A profile along either of the diverging lines may be 
plotted by the rules already given (Art. 20.) The diagram 
shows the profile along the line AB. 


A 



28. The following example will illustrate the methods 
employed in making a topographical survey, where great 
accuracy is required. 

By means of a theodolite or level, range a line of stakes 
A, B 1 G\ D , E , &c., along one side, or through the middle of 
the ground to be surveyed, at equal and convenient distances 
from each other, say 50 feet apart. Mark, with a piece of 
red chalk, on each stake in this row, one of the letters of 
the alphabet, A, B t G J D : E, &c., in their order. At A, 
range a line of stakes, perpendicular to AE, planting the 
stakes at intervals of 50 feet; and mark them with the 

letters A A A, are rea q ^ first, ^ second, 

A third, &c. 










SEC. 11.] TOPOGRAPHICAL SURVEYING. 


t 

165 

* 


A 

A 

A 

A 

A 

l 

Z 

3 

i 

4 

s 

B 

B 

B 

B 

B 

1 

2r 

3 

4 

5 



b 



C 

C 

a 

C 

c 

1 

% 

3 

4 

6 


♦ 

• 



D 

1) 

D 

J) 

1) 

1 

& 

s 

4 

6 



a 



El 

Ez 

E3 

E4 

Es 


B 


C 


D 


Ai Z?, range a line of stakes also perpendicular to AE\ 
and at distances of 50 feet from each other, and designate 

them -H &c. Do the same at (7, D 1 E\ &c., until all 

the stages are - placed, dividing the area to be surveyed 

into squares of 50 feet on a side. The letters and figures 
should be plainly marked on a smooth face of each stake, 
for facility of reference. If this system of notation be fol¬ 
lowed, the stakes may be recorded without danger of con¬ 
fusion. 

The next operation is to determine the difference of 
level between each stake, and some fixed horizontal plane, 
which is called a plane of reference. If the sea is near, the 

plane of mean low water, may be taken as the plane of 

reference. If not, assume the horizontal plane, passing 
through the lowest point of the ground to be surveyed, and 
make a permanent bench-mark at the point of beginning. 
If the lowest point cannot be easily determined, assume 
such a plane of reference as shall pass quite below the low¬ 
est point of the ground. 

In the example, which we have taken for illustration, 
the stake % is at the lowest point, and let us assume the 

u 

plane of reference to pass through that point. 









ELEMENTS OF SURVEYING. [BOOK IIL 


♦ 

166 

Set up the level at some convenient point, as a, take the 

reading of a levelling staff, set up at ^ and enter this 

reading as a back-sight. Then take the readings of the 
staff, at as many-stakes as can be reached from the posi¬ 
tion a of the level, entering them as fore-sights. Endeavor¬ 
ing to make the last reading as small as possible. At this 

last stake ^ drive a small peg for a bench-mark. 

Move the level to a second point b , and take a back¬ 
sight to the bench-mark (6T), and fore-sights, to as many 
stakes as possible. The following is the form of a field- 
book, used in topographical levelling. 


FIELD NOTES. 


Back-sights. 

Fore-Siglits. 

Difference 

Total dif'.of level 

above E 3 

Remarks. 

Object 

Reading 

Object 

Reading 



] 

Object 

Reading 








E3 

0.000 


E3 

11.432 

D3 

1.211 

+ 10.221 

D3 

10.221 




C4 

0.897 

+ 

0.314 

C4 

10.535 

Check 10.535 

C4 

11.112 

E2 

5.281 

+ 

5.831 

E2 

16.366 




E4 

6.154 

— 

0.873 

E4 

15.493 




D4 

6.001 

+ 

0.153 

D4 

15.646 




D2 

1.182 


4.819 

D2 

20.465 




C8 

2,917 

— 

1.735 

C3 

18.730 




B5 

6.080 

— 

3.163 

B5 

15.567 




C5 

0.921 

+ 

5.159 

C5 

20.726 




B4 

0.113 

-r 

0.808 

B4 

21.534 

Check 10.999 

B4 

11.882 

El 

8.019 

+ 

3.863 

El 

25.397 










21.534 



B3 

3.990 

+ 

4.029 

B3 

29.426 




Dl 

4.118 

— 

0.128 

Dl 

29.298 




C2 

1.830 

+ 

2.238 

C2 

81.536 




A4 

5.000 

— 

3.120 

A4 

28.416 




A5 

9.928 

— 

4.928 

A5 

23.488 




D5 

1.675 

+ 

S.253 

D5 

31.741 




E5 

1.111 

+ 

0.564 

E5 

32.305 




A3 

0.108 

+ 

1.003 

A3 

33.308 




Cl 

0.004 

+ 

0.104 

Cl 

33.412 

Check 11.878 

Cl 

11.149 

B2 

4.181 

+ 

6.968 

B2 

40.380 

33.412 



B1 

2.008 

+ 

2.173 

Bl 

42.553 




A2 

0.817 

+ 

1.191 

A2 

43.744 

Check 10.332 





- 




43.744 

A2 

10.102 

A1 

4.332 

+ 

5.770 

Al 

49.514 

Check 5.770 









49.514 






















SEC. II.] TOPOGRAPHICAL SURVEYING. 167 

♦ 

If we subtract the first fore-sight (D3), from the back¬ 
sight (E3), the difference, entered in the column headed 
difference , is evidently the height of (D3), above the plane 
of reference through (E3); and we accordingly enter it 
under the column headed total diff. of level , as well as in 
the column of differences. If we subtract the fore-sight 
(C4) from the fore-sight (D3), the difference, entered in the 
column of difference, is evidently the height of (C4) above 
(D3); if we now add this difference to the previous total, 
we shall find the height of (C4) above (E3). Subtracting 
the fore-sight (E2) from the back-sight (C4), we get the dif¬ 
ference of level between (E2) and (C4) which, added to the 
previous total, gives the height of (E2), above the stake 
(E3). In subtracting the fore-sight (E4) from the fore-sight 
(E2), we find a negative result which shows that (E4) is 
below (E2). We enter, then, this difference with its neg¬ 
ative sign, and to get the total, we subtract this difference 
from the previous total, and so on. 

As a check on the accuracy of our computation, sub¬ 
tract the fore-sight (C4) from the back-sight (E3), and the 
difference will give the height of (C4), above the plane of 
reference. 

Again, subtract the fore-sight (B4) from the back-sight 
(C4), and add the remainder to the height of (C4,) and we 
shall find the height of (B4), which should agree with the 
height found under the heading, total diff. of level; and so 
on for each time the level is moved. 

PLOTTING THE WORK. 

29. Draw, on a piece of paper, a straight line AE. 
From a scale of equal parts, set off distances AB , BC\ 
&c., each to represent 50 feet. Erect perpendiculars at 
each of the points A, B, C, &c., and then set off the distan¬ 
ces from A to 2, from 2 to 3, &c., each to represent 50 
feet; and through the points 2, 3, 4 and 5, draw parallels 
to AE. These, by their intersections with the lines drawn 
through A, B, C,\ &c., will determine the position of the 

stakes, ^ ^ &c.; and write in red ink on the plot, the 

If 


168 


ELEMENTS OF SURVEYING. [BOOK III 

height above the plane of reference of each stake, taken from 
the column of total differences in the field-book. Let us sup¬ 
pose that the horizontal planes are to be taken at distances 
of 6 feet. We may find the points in which the contour 



lines intersect the lines at right angles, by the previous 
method, or perhaps still better, let the Surveyor take the 
plot thus commenced into the field, and by the eye trace 
the contour lines on the map. If we note where the lines 
at right angles cut fences, roads, streams, &c., we can, by 
joining the points, obtain a plot of the ground. 

30. The contour lines may be found as follows: Set up 
the level at «, and observe that the back-sight, to the stake, 
placed at ( E2>\ gave a reading of 11.432. Depress the 
vane equal to the distance between the horizontal secant 
planes, that is, 6 feet, which is done by placing it at the 
reading 5.432. Then direct* the rodman, by signals up or 
down the hill, till the horizontal hair of the telescope coin¬ 
cides with the* horizontal line of the vane. The foot of the 
staff is then 6 feet above the first point. Let a stake, 
marked 6, be driven here, and direct the rodman around 
the hill, until a second position shall be found, when the 















SEC. II] TOPOGRAPHICAL SURVEYING. 


169 


horizontal hair of the telescope will cut the vane, and drive 
there another stake, marked 6; and so on, until a sufficient 
number of stakes have been driven to determine the curve 
(6). Then, let the line of stakes, marked 6, be surveyed 
with the compass and chain, and plotted. Other contour 
ines may be found in a similar manner. 

31. We will add another example for determining the 
contour of an undulating piece of ground (PI. 4, Fig. 
7,) by means of horizontal sections. Let rows of stakes 
DA, HE, IF, &c.,.be driven at intervals, depending upon 
the required accuracy of the survey, and let f g, h, &c., 
be stakes driven along the lines, at such points as will 
best show the accidents of ground. Determine as before 
the difference of level between each stake, and some fixed 
point, and then determine where the contour lines cut the 
lines AD, EII, &c., by the rules already laid down. 

After the stakes are all placed, and the distances meas¬ 
ured, let the differences of level of all the points so desig¬ 
nated be found. In the present example, the results of the 
measurements are, 


Aa — 80 
ab = 60 

be = 90 
cd = 55 
dD =50 


AE= 100 
Ef = 105 
fg = 85 
gh = 71 
hll= 74 


EF= 100 
Fi = 74 
ik — 115 
kl = 60 
II = 86 


FG = 100 
Gm— 96 
mn = 76 

np = 76 

pL = 87 


GB= 100 
Bq = 76 
qs = 85 
st = 127 
tC = 47 


Of the Levelling. 


Line EH 


Line FI. 


Line GL. 


Line AD. 

Ft. 

A above CL 5 
a “ b 6 
b “ c 7 

C below d 2 
d above D 4 


E below A 3 

B above J 9 

/ 11 9 3 
g 11 hi 
h below II 3 


Ft. 

j^below E 2 

F above % 3 

i 11 k 5 
k “ 1 2 

l below I 3 


Ft. 

G below F 1 
G above 771 2 
m u n 1 
n 11 p 2 
p) below L 4 


Line BO. 

Ft. 

B below G 2 

B above q 3 

q u s 2 
5 “ 1 3 

t below C 5 


The heights of the points are here compared with each 
other, two and two. Before, however, we can conceive 










170 


ELEMENTS OF SURVEYING. [BOOK IIL 


clearly their relative heights, we must assume some one 
point, and compare all the others with it. Let the point 
A be taken. The height of 





Ft. 



• 

4 

Ft. 




Ft. 




Ft. 

A above 

a 

5 

A above/ 

12 

A above Jc 

13 

A abovey> 

11 

A 

a 

b 

11 

A 

tt 

9 

15 

A 

it 

l 

15 

A 

a 

L 

7 

A 

It 

c 

18 

A 

a 

h 

16 

A 

a 

I 

12 

A 

it 

B 

8 

A 

It 

d 

16 

A 

a 

H 13 

A 

a 


6 

A 

it 

9 

11 

A 

tt 

B 

20 

A 

It 

F 

5 

A 

it 

m 

8 

A 

it 

s 

13 

A 

tt 

F 

3 

A 

It 

• 

i 

8 

A 

it 

n 

9 

A 

it 

t 

16 


.And of A above (7, 11 feet. 


This being done, a mere inspection shows us the high¬ 
est and lowest points, as also the relative heights of the 
others, reckoning upwards or downwards. Let them be 
now written in the order of their heights above the lowest 
point, which is B. The difference of level between A and 
B being 20 feet, if the difference of level of each of the 
points below A, be taken from 20 feet, the remainder will 
be the height above B. Arranging them in their order, 
we have 





Ft 




Ft. 




Ft. 




Ft. 

c 

above D 

2 

H above D 

7 

JO 

xbove B 

9 

i?above B 

12 

d 

it 

D 

4 

Jc 

a 

D 

7 

9 

a 

B 

9 

L 

tt 

B 

13 

h 

a 

D 

4 

s 

tt 

I) 

7 

C 

it 

B 

9 

G 

tt 

B 

14 

t 

a 

D 

4 

f 

it 

D 

8 

n 

l( 

B 

11 

a 

it 

B 

15 

9 

tt 

D 

5 

I 

it 

B 

8 

i 

• 

a • 

B 

12 

F 

tt 

B 

15 

l 

it 

D 

5 

b 

it 

B 

9 

m 

a 

B 

12 

F 

it 

B 

17 


A above D , 20 feet. 


In this example, the plane of reference is assumed 
through J9, the lowest point of the ground; and the secant 

planes are taken 3 feet apart. 

«• 

32. The manner of shading the map, so as to indicate 
the hills and slopes, consists in drawing the lines of shad¬ 
ing perpendicular to the horizontal curves, as already ex¬ 
plained. These shading lines are drawn close together, 
when the slope is abrupt, and further apart, as it grows 
more gentle. Fig. 7 indicates the method of shading. 








SEC. II.] TOPOGRAPHICAL SURVEYING. 


171 


33. When the plane of reference is so chosen that the 

points of the work fall on different sides of it, all the re¬ 
ferences on one §ide are called positive, and those on the 
other, negative. The curves having a negative reference 
are distinguished by placing the minus sign before the 
number ; thus — ( ). 

34. In topographical surveys, great care should be taken 
to leave some 'permanent marks , with their levels written 
on them in a durable manner. For example, if there are 
any rocks, let one or more of them be smoothed, and the 
vertical distance from the plane of reference marked there¬ 
on: or let the vertical distance of a point on some promi¬ 
nent building, be ascertained and marked permanently on 
the building. Such points should also be noted on the 
map, so that a person, although unacquainted with the 
ground, could by means of the map, go upon it, and trace 
out all the points, together with their differences of level. 

35. Besides representing the contour of the ground, it 
is often necessary to make a map which shall indicate l^je 
cultivated field, the woodland, the marsh, and the winding 
river. For this, certain characters, or conventional signs, 
have been agreed upon, as the representatives of things, 
and when these are once fixed in the mind, they readily 
suggest the objects for which they stand. Those which 
are given in Plates 5 and 6, have been adopted by the 
Engineer Department, and are used in all plans and maps 
made by the United States Engineers. 

It is very desirable that a uniform method of deline¬ 
ation should be adopted, and none would seem to be of 
higher authority than that established by the Topographi¬ 
cal Bureau. It is, therefore, recommended, that the con¬ 
ventional signs given in Plates 5 and 6, be carefully 
studied and uniformly followed. 

/ ’*<> 

;4 ‘'i ) 


BOOK IV. 


GEODESIC, TRIGONOMETRIC AND MARITIME 

SURVEYING. 

' N ' £ 


SECTION I. 

GEODESIC AND TRIGONOMETRIC SURVEYING. 

1. When a large extent of territory, or a long line of 
sea-coast is to be surveyed, it becomes necessary to con¬ 
sider the curvature of the earth’s surface; this branch of 

surveying is called Geodesic surveying. 

% 

2. Extensive geodesic operations prove that the earth 
is an oblate spheroid, the shortest diameter of which coin¬ 
cides with the terrestrial axis, and all of whose meridians, 
are equal ellipses. The meridian lines, however, differ so 
little from the circumferences of circles, that they may be 
taken for them, except when great accuracy is required. 
The earth, will, therefore, in the following pages, be re¬ 
garded as a perfect sphere. 

3. The operations necessary to the successful execution 
of a Geodesic Survey, require the minutest attention, and 
when performed, numerous corrections are to be applied to 
the measured lines and angles, on account of the various 
causes of error incident to such operations. 

To investigate those causes of error, and to deduce rules 
for correcting the errors, in all cases, would far exceed 
the limits of an elementary treatise. We shall, therefore, 
attempt nothing more than a brief outline of the operations 



SEC. I.] 


TRIANGULATION. 


173 


of a trigonometric survey, with the application of some of 
the more important corrections. 

4. It may be observed that most of the operations de- 
. scribed in this section, are equally applicable, whether we 

regard the area surveyed as plane or spherical: in either 
case, the basis of an accurate survey, is an extensive sys¬ 
tem of triangulation. 

5. After having made a preliminary examination or re - 
y connaissance of the territory to be surveyed, suitable statipns 

are selected at the most prominent points, and these points 
are marked by staves or signals. 

A base line is then measured. The length of the base 
will, in general, depend upon the magnitude of the survey, 
and each extremity is marked by a signal. 

The next step is the triangulation . At each extremity 
of the base, the angles between the base, and the lines 
drawn to each of the visible signals, are carefully meas¬ 
ured by means of a theodolite. The sides of the triangles 
thus obtained, serve as new bases upon which other trian¬ 
gles may be formed, and so on, until the entire area is 
covered by a net-work of triangles. 

6. This system of triangles is called the 'primary system, 
and the operation of forming them is called the primary 
triangulation. Within the primary triangles, and depending 
upon them, a system of smaller triangles is formed in the 
same manner, called the secondary system ; and if the extent 
or importance of the work should demand it, the secondary 
may be sub-divided into tertiary triangles. 

Having completed the triangulation, the characteristics 
of the surface, such as roads, streams, villages, boundaries, 
&c., are filled in by means of the compass, plain table, or 
some of the methods already explained. 

After the field work is completed, the triangles, when 
regarded as spherical, are reduced by applying the formula 
for spherical excess, hereafter explained, and other neces¬ 
sary corrections, and thus the whole work is plotted upon 
paper. 


174 


ELEMENTS OF SURVEYING. [BOOK IV. 


PRELIMINARY RECONNOISSANCE AND ESTABLISHMENT OF 

SIGNALS. 

« 

7 . Before commencing a trigonometrical survey, an ex¬ 
amination of the entire territory should be made for the 
purpose of selecting a location for the base line, and proper 
points for stations; this examination should be more or 
less elaborate, according to the nature and extent of the 
survey. 

The proper distribution and combination of the trian¬ 
gles, so as to adapt them to the survey in hand, require 
great judgment and care, and but few rules can be given for 
the selection of trigonometrical points. Those points should, 
in general, be chosen in such a manner, that they may be 
distinctly visible from each other, and so that the triangles 
formed, by uniting them, may be as nearly as possible 
equilateral. 

It is easily seen, that a triangle which has an obtuse 
or a very acute angle, will experience a greater change of 
form for a given error, than one which is nearly equilate¬ 
ral ; and since the accuracy of each triangle depends upon 
the preceding ones, it is further evident, that the introduc¬ 
tion of a single ill-conditioned triangle, might vitiate the 
whole survey. Except in extreme cases, no angle, less than 
30°, should be used, and even angles of 30° should not be 
admitted when the locality can be so chosen as to prevent 
it. The base is usually much shorter than the sides of the 
primary triangles; these sides, however, should be increased 
as rapidly as is consistent with the above remarks. 

8. The accompanying diagram will illustrate the man¬ 
ner of increasing the sides without introducing ill-con¬ 
ditioned triangles. Having measured the base AB 1 and the 
requisite angles, the triangles ABO and ABB , may be de¬ 
termined, and the line DC computed; with DO as a base, 
the triangles DOE and DOF are formed, and thence EHF\ 
and EGF : in which the sides are much greater than the 
base AB. 


SEC. I.] 


SIGNALS. 


175 



In this manner the sides may be increased to any de- 
sirable extent. An ordinary map of the country, or a 
sketch made with the pocket compass, will be of material 
assistance in making a proper distribution of the stations. 

9. The stations are marked by signals, which may be 
constructed in a great variety of ways, depending upon the 
locality of the stations, and the lengths of the sides of the 
triangles. 

Sometimes a signal has to be raised above the level of 
the adjacent country, in which case it is constructed of 
timbers, and upon the apex, is placed a vertical staff, bear¬ 
ing a flag. The exact trigonometrical point is. determined 
by a plumb-line, suspended from the apex of the signal. 

A temporary signal may be constructed with three or 
four pieces of scantling framed and traced, 
as shown in the annexed figure, wifh a short 
pole projecting from the apex. The plumb 
determines the point B 1 which is the exact trig¬ 
onometrical point over which the theodolite 
is to be placed. Where the sides of the trian¬ 
gles are not very great, a pole, planted ver¬ 
tically, and surmounted by a flag, will an¬ 
swer as a signal. 

In order to distinguish the different signals, the flags 
which they bear, should be different from each other. 
They may be formed by arranging stripes -of white and 








176 


ELEMENTS OF SURVEYING. [BOOK IV. 


red, according to some pre-arranged plan, and the flags of 
the different stations should be entered in a book. For 
the purpose of future reference, the trigonometrical point, 
at each station, as B , should be indicated by a permanent 
mark. If the point falls upon a rock, a hole may be drill¬ 
ed to show the locality; or if not, a mark-stone may be 
sunk under the point, deep enough to be beyond the reach 
of accident. A record of the monument should be pre¬ 
served, together with its reference to some of the perma¬ 
nent objects in the neighborhood. 

In order to render the signals visible from the distant 
stations, polished tin plates are sometimes attached to the 
signal-post, so as to reflect the sun towards the stations at 
certain hours of the day. The Drummond-light has also 
been used to show very distant stations. A light may also 
be produced that can be seen at a distance of 60 or 70 
miles, by placing a ball of lime about a quarter of an inch 
4 in diameter, in the focus of a parabolic reflector, and heat¬ 
ing it intensely by a stream of oxygen gas, directed by a 
blow-pipe, through a flame of alcohol. If obstacles, as trees, 
and under-brush intervene, vistas have to be opened along 
the lines, from station to station. 

• MEASUREMENT OF A BASE LINE; 

10. The measurement of a base line on which the ac¬ 
curacy of the entire survey depends, is one of the most 
difficult operations of geodesic surveying, and one, for the 
successful accomplishment of which, art and science have 
been strongly taxed. The selection of a proper site for a 
base line, forms one of the first objects of the preliminary 
reconnaissance. It should, if possible, be fixed on an open 
plain. It must be so chosen, that the surrounding signals 
may be distinctly seen from its extreme points; and hence, 
those signals which mark points of the adjacent triangula 
tion, should be selected with reference to the base. The 
length of the lase , should, in a measure, depend upon the 
magnitude of the survey, though circumstances seldom 
admit its being taken more than 6 or 8 miles in length. 


SEC. I] 


BASE LINE. 


177 


11. Different instruments have been used for measuring 
base lines, sucb as steel chains, glass, platinum and deal 
rods; and more recently, a combination of rods, of differ¬ 
ent metals, so adjusted, that the apparatus maintains an in¬ 
variable length at all temperatures. This last mentioned 
apparatus, has been much improved, and most successfully 
used by Prof. Bache, in the Survey of the United States* 
Coast. 

12. In minor surveys, where the base line does not 
much exceed 1000 or 2000 feet, sufficient accuracy may be 
attained by the use of wooden rods. To render the rods 
less susceptible of change, from moisture, they* should be 
saturated with boiling oil, and covered with a thick coat¬ 
ing of varnish. 

The ends of the rods should be protected by metallic 
caps, which prevent their wearing, and insure a more per¬ 
fect contact. 

When the rods are prepared for use, they should be 
carefully compared with some standard measure, and from 
time to time this comparison should be repeated, in order 
to detect any minute change of length, should such change 
take place. 

13. The following method of measuring a base line of 
1000 or 2000 feet, may be rendered very accurate. 

Having decided upon the direction of the base, and 
measured it carefully, two or three times with a chain, let 
a theodolite be planted at one end of the line, and direct¬ 
ed upon a flag, planted at the other. Then, by means of 
the vertical limb, let a row of pickets be driven along the 
base, taking care to plant them at a distance from each 
‘other, equal to the length of one of the deal rods. Then, 
plant in the place of each picket, a vertical post, 6 or 8 
inches in diameter, and projecting a sufficient distance 
above the surface of.the ground. If necessary, let the 
posts be steadied by heaping about them, earth or stones. 
Next, with the assistance of a spirit-level, let each post be 
sawed o(f, so as to bring their'tops to the same horizontal 

12 


178 


ELEMENTS OF SURVEYING. ' [BOOK IV 


plane, and by means of the theodolite, let a line be marked 
on the top of each post, in the direction of the base. 
This line will determine the direction in which the rods 
are to be placed, and the contact of the ends must all be 
on this line. 

The contact of the rods should be made with great care, 
so as to avoid moving the rod already established; and 
this will be more readily done, when three rods are used. 
The measurement should be repeated two or three times 
to guard against error. 

14. If the nature of the ground does not admit of the 
posts being brought to a level, let them, by means of the 
theodolite, be brought into an oblique plane AB, and after 


B 



having measured, as before, the line AB : determine accu¬ 
rately the difference of level between the points A and B, 
equal to BC\ then, from the right-angled triangle ABC. we 
should find the horizontal distance AC — V AB i — BC'. 

15. In very extensive surveys, the base should be several 
miles in length, and the apparatus for measurement, as well 
as the operations on the field, become more complicated. 
For a full description of a very perfect base apparatus, and 
the method of using it, the reader is referred to Prof. 
Bache’s pamphlet, on the subject—the details of the descrip¬ 
tion would exceed our limits. * 

TRIANGULATION. 

16. The theodolite is generally used for measuring the* 
angles of a trigonometric survey. The extent of the survey, 
and the standard of accuracy to which the results are re¬ 
quired to conform, must determine the size and perfection 
of the instrument to be employed. The angles of the pri¬ 
mary triangles of the United States Coast Survey, nre meas¬ 
ured with theodolites, whose horizontal circles are 2.4 or 80 














SEC. I] 


TRIANGULATION. 


179 


inches in diameter; and to eliminate as much as possible, 
every source of error, great numbers of operations are made 
on each station, the readings being made on different points 
of the arc. Usually from 40 to 60 observations are made 
for each angle—one measurement, with the telescope direct* 
and one with it reverted, constituting a complete observa 
tion. With these precautions, it has been found that the 
error in a primary triangle (where the sum of its three an¬ 
gles has been compared with 180°), has fallen much with¬ 
in 3 seconds. The error of 3 seconds has been adopted as 
the highest admissible limit of error. 

17. Observations are also made at the principal stations 
upon the pole-star, and other stars near the pole, for the 
purpose of determining the angle, made by the sides of the 
triangle with the meridian. In minor surveys, and in a 
secondary triangulation, the operations are much less elabo¬ 
rate ; still, every precaution is to be taken to insure the 
greatest attainable accuracy. As a general rule, all the an¬ 
gles of every triangle, should be measured, if possible. 

18. To illustrate the manner of carrying on a minor 
triangulation, let us refer to the plan of the harbor [plate 
6], in which AB is the measured base, (7, A, A, &c,, tri¬ 
angulation points, at which signals have been erected. 
Commence the triangulation at A , the west end of the 
base; and for convenience in plotting, it would be well 
to make the line, passing through the 0 point, and 180° 
parallel, in each position of the instrument, to the base 
AB. Having brought the 0 of the vernier to the 0 of the 
limb, clamp the vernier plate, and direct the upper teles¬ 
cope to the signal at A, and clamp the limb. Enter the 
observation as in the following table: 

OBSERVATION AT STATION A. 


Name of Station. 

Vernier I. 

Vernier IT. 

Mean. 

Station B 

o 

o 

o 

o 

o 

o 

o 

O 

o 

-s. 

o 

o 

o 

o 

o 

o 

o 

o 

o 

Station E 

72° 24' 55" 

25' 5" 

72° 25' 00' 

Station Gr 

138° 34' 56" 

35' 4" 

l—i 

co 

GO 

o 

CO 

Oi 

o 

© 

&c. 

&c. 

&c. 

&c. 
















180 'ELEMENTS OF SURVEYING. [BOOK IV. 

Haying recorded the reading of the first vernier, and 
the minutes and seconds of the second vernier, unclamp 
the vernier plate, and direct the telescope to the station at 
E, and record both verniers, as before. Again unclamp the 
vernier plate, and direct the telescope on the signal at G ; 

and then read and record, as before. 

• 

Having determined the angles subtended by all the 
signals visible from A, let the theodolite be removed to 

B. Bring the 0 of the vernier I to 180° on the limb, and 
direct the telescope on the signal at A —the line (0°, 180°) 
will then be parallel to its first position, and the limb may 
be clamped. Bead now the angles to the signals at A, E\ 

C, \ &c., and record as before. 

If the theodolite is now removed to the station E, the 
line (0°, 180°), may be made parallel to its first position, 
by adding 180° to the reading of the first vernier, from A 
to A, and then directing the telescope on the signal at A. 
The line (0°, 180°), will thus be made parallel to AB, and 
the reading may be made and recorded as before; and 
so on until all the stations have been visited, and the an¬ 
gles measured. From the field records, the angles BAE\ 
EAG, ABE, EBG , &c., may be easily deduced, the whole 
may be plotted on paper, or the several sides may be com¬ 
puted trigonometrically. It may be observed that the line 
(0°, 180°), has been made parallel to the base line at each 
station; where great accuracy is required, this cannot be 
done, since a single reading is insufficient to give the angle. 
The angle is then determined, as directed in the previous 
article, or by means of the principle of repetition. 

19. To illustrate this principle of repetition, suppose the 
0 of the vernier to coincide with the 0 of the limb, and the 
telescope to be directed, from the station A, upon one of the 
objects, as the signal at B. Clamp the limb, and unclamp¬ 
ing the vernier plate, direct the telescope on the second ob¬ 
ject, as the signal at E. If we now clamp the vernier 
plate, and unclamping the limb, direct the telescope on the 
signal at B, the line (0°, 180°), of the limb, will make 
with AB, an angle equal to BAE. Again clamp the limb, 


SEC. I] 


TRIANGULATION. 


181 


and unclamping the vernier plate, direct the telescope on 
the signal at E. The reading will evidently he equal to 
twice the angle BAE\ and if we repeat the operation, the 
reading will be three times the angle, and so on. After 
ten repetitions, if we add 860° each time the 0 of the 
vernier passes the 0 of the limb, the final re&ding will be 
ten times the angle BAE, affected with the joint errors of 
•'he ten observations, and one-tenth of this will be the read¬ 
ing required, to a greater degree of accuracy than could 
probably be attained by a single observation. 

20. The method of reading angles, by this mode, is as 
follows: 

• • 

Angles at station A, between signals B (left), and E 
(right.) 


June 8th, 1851. 


No. of Repe¬ 
titions. 

Vernier I. 

Vernier 

II. 

Mean of Verniers. 


1 

72° 24' 55" 

25' 5" 

72° 25' 00" 


2 

144° 49' 55" 

50' 0" 

144° 49' 58" 


3 

217° 14' 50" 

15' 10" 

217° 15' 00" 


4 

289° 39' 50" 

40' 00" 

289° 39' 55" 

4)289° 39'55" 




Mean reading 

72° 24' 59" 


FILLING UP THE SURVEY. 

21. After the triangulation is completed, the interior 
may be filled up by the aid of the Compass, or the plane- 
table. 

USE OF THE COMPASS. 

22. When the secondary and tertiary triangles have been 
considerably multiplied, the compass is taken in hand. 
The field-notes may be kept in the following manner. Di¬ 
vide a page of the note-book into two equal parts,* by two 
parallel lines near to each other, and consider each part as 
a separate leaf or page. Each leaf is divided into three 















I 


182 , ELEMENTS OF SURVEYING. [BOOK IV 

spaces, and the middle space is generally smaller than either 
of the others, which are equal. 

The notes begin at the bottom.of the first page, and 
run up the page to the top. They then commence again 
at the bottom of the next page, and run up to the top; 
thence to th& bottom of the third page, and thus, for as 
many pages as the work may require. 

When the compass is used in the way we are about to 
explain, the distances to objects which lie on the right or 
left of the courses, are determined by means of offsets. 

The beginning of every course is designated in the mid¬ 
dle column by 0, and the bearing is entered directly above. 
The other figures of the middle column, express the dis¬ 
tances from the ‘beginning of each course to the offsets, and 
those in the side columns indicate the lengths of the offsets, 
or the distances to objects on the right or left of the com¬ 
pass lines. 

To explain more definitely the manner of using the 
compass on the field, let us suppose that we have deter¬ 
mined the prominent points and longer lines with the 
theodolite. Place the compass at A (Plate 6), and take the 
bearing of the line AE, which is S 12° W. 



Enter this bearing at A. Then measure along the line 

































. SEC. I.] 


THE PLANE-TABLE. 


188 


AE any distance, as Aa equal to 130 yards, and make an 
offset to the lake, which, we measure and find to be 50 
yards. Enter the 130 in the middle column, and as the 
lake lies on the right (in going from A to E), we insert 

the 50 in the right hand column. 

» 

We then measure along the line AE to b, 350 yards 
from A. Here we make a second offset to the lake, and 
find it to be equal to 100 yards. Having entered the dis¬ 
tances in the notes, we measure to q, the point where the lint> 
AE crosses the creek, and we enter the distance from A, 
415 yards. 

At d, we lay off an offset on the left, to the pond, 70 
yards: at e, an offset to the mouth of the creek, 150 yards: 
and at A, where the course terminates, an offset to the 
lake, of 160 yards. The entire distance from A to A is 
800 yards. 

At A, we take the bearing to H, which is JST 50° E. 
Having measured along this line to f 315 yards, we make 
an offset to the pond, on the left, of 50 yards, and to the 
shore, on the right, of 90 yards. Having entered these 
distances, we recommence the notes at 315 below, which we 
suppose to be at the bottom of the second page. Having 
reached H, the extremity of the course, we enter the en¬ 
tire distance from A, 680 yards. We next take the bear¬ 
ing to 7j S 52° E. We then measure the distances to m, 
w, p, and I, and enter them, together with the offsets, as 
in the notes. 

23. It is also well to make, in the columns on the right 

and left, such sketches of the ground, fields, houses, creeks 
and rivers, as will afford the means of making an accu¬ 
rate delineation on paper. y 

THE PLANE-TABLE—ITS USES. 

24. PI. 3, Fig. 1. The plane-table consists of two parts; 
a rectangular board CDBA : and a tripod EHG , to which 
it is firmly secured. 

Directly under the rectangular board are four milled 
screws which pass through sockets inserted in a horizontal 


184 ELEMENTS OF SURVEYING. [BOOK IV. 

brass plate : these screws are worked against a second ho¬ 
rizontal plate, for the purpose of levelling the table; the 
table having a ball and socket motion, similar to the limb 
of the theodolite. 

For the purpose of levelling the table, a small detached 
spirit-level is used. This level being placed over the 
centre, and also over two of the levelling screws, the screws 
are turned contrary ways until the level is horizontal; 
after which, it is placed over the other two screws, and 
made horizontal in the same manner. 

Between the upper horizontal plate and the table, there 
is a clamp-screw, similar to the clamp-screw of the theodo¬ 
lite, which Being loosened, the table can be turned freely 
about its axis. There is, also, a small tangent-screw, by 
which the smaller motions of the table are regulated, after 
the clamp-screw is made fast. Neither of these screws can 
be seen in the figure. 

The upper side of the table is bordered by four brass 
plates, about one inch in width, and the centre of the table 
is marked by a small pin, F. About this centre, and tan¬ 
gent to the sides of the table, conceive a circle to be de¬ 
scribed. Suppose the circumference of the circle to be di¬ 
vided into degrees and parts of a degree, and radii to be 
drawn through the centre and the points of division. The 
• points in which these radii intersect the outer edge of the 
brass border, are marked by lines on the brass plates, and 
the degrees are numbered in the direction from left to 
right, from the point L to.the point 7, 180°, and from the 
point I to the point L, 180°. In some plane-tables, how¬ 
ever, they are numbered from 0 to 360°. 

There are, generally, diagonal scales of equal parts cut 
on the plates DLC and AIB ,, the use of which will be ex¬ 
plained hereafter. 

Near the two other edges of the table, two small grooves 
are made, into which the plates of brass DB and CA are 
fitted, and these plates are drawn to their places by means 
of milled screws, which pass through the table from the 
under side, and screw firmly into the plates. The heads 


SEC. I.] 


THE PLANE-TABLE. 


185 


of two of the screws, Q and S, are seen in the figure, as 
also one of the plates and its two screws in Fig. 8. The 
object of these plates is to confine a sheet of paper on the 
table. By loosening the screws, and pressing them up¬ 
wards, the plates are raised above the surface of the table; 
the edges of the paper can then be placed under them: 
then, by turning the screws back again, the plates are 
drawn down and the paper held tightly. Fig. 1 represents 
the table with the paper partly put upon it: one edge of 
the paper has been placed under the j^late DB , and the 
screws S and tightened. The paper, before being put 
on, should be moistened, in order to expand it; and then, 
after it has been dried, it will fit closely to the table. 

A ruler, AB (Fig. 2), with open vertical sights, is used 
with the plane-table. This ruler has a fiducial edge, which 
is in the same vertical plane with the hairs of the sights. 
A ruler with a telescope, and a vertical limb, similar to the 
vertical limb of the theodolite, is sometimes used with the 
plane-table. A compass, also, is often attached to the table, 
to show the bearings of the lines. 

The plane-table is used for two distinct objects. 

1st. For the measurement of horizontal angles. 

2dly. For the determination of the shorter lines of a 
survey, both in extent and position. 

TO MEASURE A HORIZONTAL ANGLE. 

25. Place, by means of a plumb, the centre of the table 
directly over the angular point: then level the table; after 
which, place the fiducial edge of the ruler against the small 
pin at the centre : direct the sights to one of the objects, 
and note the degrees on the brass plate ; then turn the 
ruler and sights to the other object, and note the degrees 
as before. If the ruler has not passed over the 0 point, 
the difference of the readings is the angle sought; but, if 
it has, the larger taken from 180°, and the remainder added 
to the smaller, gives the required angle. 

TO DETERMINE LINES IN EXTENT AND POSITION. 

26. Having placed a paper on the table, examine the 


186 


ELEMENTS OF SURVEYING. [BOOK IV. 

objects and lines which are to be determined, and select 
for a base a convenient portion of such a line of those 
already formed in the triangulation, that most of the ob* 
jects can be seen from its extremities. Then place the 
plane-table with its centre, nearly, though not accurately, 
over one extremity of the base; make it truly horizontal, 
and turn it until the larger part of the paper lies on the 
same side of the base with the objects. 

Then, tighten the clamp-screw, and mark with a pin the 
point of the paper directly over the station, which point is 
determined most accurately by suspending a plumb from 
the lower side of the table. Press the pin firmly on this 
point, bring the fiducial edge of the ruler against it, and 
sight to the other extremity of the base line, and mark 
with the pin or pencil, the direction of the line on the 
paper. Sight in like manner to every other object, and 
draw on the paper the corresponding lines, numbering them 
from the base line, 1, 2, 3, 4, &c. 

Then, with a pair of dividers, take from the scale a 
certain number of equal parts to represent the base, and 
lay off the distance on the base line from the place of the 
pin. Take up the table, carry it to the other extremity 
of the base, and place the point of the paper correspond¬ 
ing to that extremity, directly over it. Place the fiducial 
edge of the ruler on the base line, and turn the table, by 
means of the tangent-screw, until the sights are directed to 
the first station. If, however, in bringing the table to this 
position, the corresponding point of the paper has been 
moved from over the extremity of the base line, move the 
legs of the tripod until it is brought back to its place. 
Let the table be then levelled, after which, place the ruler 
again on the base line, and bring the table to its proper 
position by the tangent-screw, and continue the adjustment 
until the extremity of the base line on the paper is directly 
over the station, and in the same vertical plane with the 
base line on the ground. Then direct the sights to all the 
objects sighted to from the other station, and mark the 
lines 1, 2, 3, 4, &c., from the base line, as before. The 
intersections of the corresponding lines 1,1, 2,2, 3,3, 4,4, 


SEC. I] 


THE PLANE-TABLE. 


187 


&c., determine, on tlie paper, the positions of the several 
objects; and a reference of these lines to the scale of equal 
parts, determines the true distances. 

27. Let it be required, for 
example, to determine, bj 
means of the plane-table, the 
relative positions of several 
houses. 

From station A, and on 
one of the lines of the tri¬ 
angulation, as AB, measure 
the base line AN, which we will suppose equal to 800 
yards. Place the plain-table at A, and sight to the corners 
of the houses, and mark the lines 1, 2, 3, 4, &c. Then 
remove the table to JV, and sight to the same corners as be¬ 
fore, and draw the lines as in the figure. The points at 
which they intersect the corresponding lines before drawn, 
determine the corners of the houses. The front lines of 
the houses may then be drawn on the paper. Draw lines 
at right angles -to the front lines, and on them lay off the 
depths of the houses, with the same scale as that used for 
the base line. 

To find the length of any line drawn on the paper, as 
the line 1, drawn through A, for example, place the divi¬ 
ders at A and extend them to the other extremity of the 
line, and then apply the line to the scale. The length of 
the line 1 is equal to 198 yards. 


28. In this example, we de¬ 
termine from the base line 
CD, the positions of the points 
F, F] and II. 




OF CHANGING THE PAPER. 

29. When one paper is filled, and there is yet more 
work to be done, let the paper be removed, and a second 
paper put on the table; after which, the table may be 
used as before. 






188 


ELEMENTS OF SURVEYING. [BOOK- IV 

Now, in order tliat the two papers may be put toge¬ 
ther and form one entire plan, it is necessary that two 
points determined on the first paper, be also determined 
on the second; and then, by placing the lines joining 
these points, one on the other, all the lines on the two 
papers will have the same relative position as the corres¬ 
ponding lines on the ground; and the same for as many 
papers as it may be necessary to use. If different scales 
are used, the corresponding points will not join, and then 
the work must be. reduced to the same scale, before the 
papers can be put together. 

In the first example, the position of the point F was de¬ 
termined, in order to unite the first paper with the second. 

In the second example, we sighted from C and D, the 
extremities of the base line, to the points N and F\ we 
thus determined the line NF on the second paper. Pla¬ 
cing the line NF of the one paper on NF of the other, we 
have the following plan. 



In this plan, all the points and lines are accurately laid 
down. Any number of papers may be joined in the same 
manner. 

80. The principal use of the plane-table is for the in¬ 
terior filling up of trigonometrical surveys; it is also used 
with advantage, when only a plot of a field is wanted. 

It ought not be used for the determination of long lines, 
nor can it be relied on for determining extended areas. 

Having finished the field-work, some corrections are ne¬ 
cessary, before plotting the survey. The principal correc¬ 
tions are, the reduction to the centre of the station, and 
the correction for spherical excess. 




SEC. I.] 


CORRECTIONS. 


189 


REDUCTION TO THE CENTRE. 

81. It sometimes happens that fixed objects, as steeples, 
towers, and the like, are used instead of signals, in a sur¬ 
vey. The theodolite cannot be placqd over the centre of 
such stations. In all such cases, the instrument must be 
planted as near as possible to the station; then the angles, 
subtended by the various objects being measured, the true 
angle subtended at the centre of the station, is computed 
by the following formula. 

Suppose A, B and G, to be 
the three stations. Let us sup¬ 
pose that the theodolite cannot 
be placed over G, but that it 
can be placed at D, a point 
near C. 

Let the angles ABB and AD 0 be 
measured; also the distance CD, and 
the distances AG and BG computed, 
approximatively, from the side AB and 
the angles A and B. The true angle 
AGB may then be found. 

For, AEB — AGB + GAD (Geom., Bk. I., Prop. 25, 0. 6); 
and AEB = ADB + DBG : 

hence, by equating the equal values, 


or, 


A GB + GAD = ADB + DBG, 

AGB = ADB -f DBG- GAD. 

But, 

BG 

: CD :: sin BDG : sin DBG] 

or, 


sin DBG — sin BDG: 

and 

AC 

: CD : : sin ADG : sin GAD] 

or, 


CD 

sin GAD = -jn sin ADG. 


Hence, by substitution, we have 

/ CD CD \ 

AGB — ADB + y-gQ sin BDG— sin ADG) ; 

for, since the distance DC is very small in comparison with 
BO and AG, the angles DBG and GAD are very small; 
and hence, their sines may be substituted for the angles 
themselves. 


A B 



C D 






190 ELEMENTS OF SURVEYING. [BOOK IV. 

It is to be observed, that when the radius is unity, in 
the above formula, the natural sines of the angles are used, 
and that the correction within the parenthesis, is expressed 
in linear units, and will be positive or negative, according 
as the second term is less or greater than the first. 

To convert the linear correction into seconds of an arc, 
whose radius is unity, let the deduced correction, within 
the parenthesis, be denoted by c. Then, since the radius 
is 1, we shall have 

length of semi-circumference 
: the linear correction 
: : the number of seconds in 180° 

: the number of seconds in the correction: 
that is, denoting the number of seconds in the correction 
by n, 

3.1416 : c :: 648000" : n; or n = c X 206264.3" : 

c will, in all cases, be a very small fraction. 

This correction is not often necessary, for in extensive 
operations, such stations are chosen as will allow of the 
measurement of all the angles, and in secondary triangles, it 
is admissible to measure only two of the angles. '* 

SPHERICAL EXCESS. 

32. It has already been noticed, that the triangles meas¬ 
ured, are on the surface of a sphere, and consequently, the 
angles taken between any three points, by & theodolite, are, 
strictly speaking, the angles of a spherical triangle ; hence, 
the sum must exceed 180°, (Greom., Bk. IX., P. 14). This ex¬ 
cess is called the spherical excess . In the processes of trian¬ 
gulation, we reduce all triangles to rectilineal triangles; and 
hence, the sides of the triangle, which we seek, are chords 
of the sphere, and not arcs measured on the surface. 

33. In small triangles, where the sides do not exceed 
6 or 8 miles, the spherical excess may be altogether ne¬ 
glected; but in large triangles, it must be taken into ac¬ 
count. Of all the methods, yet known, of correcting for 
the spherical excess, Legendre’s is considered the best. 


SEC. L] 


SPHERICAL EXCESS. 


191 


This method is based upon the proposition that, the area 
of a spherical triangle , which is very small when compared 
with the entire surface of the sphere , is nearly identical with a 
rectilineal triangle , • whose sides are of the same length as those 
of the spherical triangle , and zuhose angles are each diminished 
by one-third of the spherical excess. 

84. The first thing, then, is to find the spherical ex¬ 
cess, and for this, we must know the area of the triangle. 
The rules for determining the area of the rectilineal trian¬ 
gles, will afford results sufficiently near, and the first ap¬ 
proximate area may be computed in square feet, as though 
the triangle were rectilineal. Having found this area, the 
formula of Legendre, gives the logarithm of the spherical 
excess, estimated in seconds, equal to the logarithm of the 
area of the triangle computed in square feet, minus the 
constant logarithm 9.326770. That is, if we put 

E — the spherical excess, in seconds. 

A = area of the triangle, in square feet. 

Constant log. = 9.326770; 

we shall have, 

Log E= log A - 9.326770. 

Having found the spherical excess, we divide it by 3, 
and then diminish each angle of the triangle by the quo¬ 
tient ; the sum of the three angles should then be equal to 
180°. With these new angles, we compute all the parts of 
the triangle. 

.85. The spherical excess between latitude 25° and 45°, 
is about 1" for an area of 75.5 miles; hence, to obtain a 
close approximation to the spherical excess, divide the num¬ 
ber of square miles in the area of the triangle by 75.5, the 
quotient will be the number of seconds required. 

36. To find the spherical excess, knowing the two sides 
a and b, and the included angle 0. 

a b sin C. 

2 B 


area = 



192 


ELEMENTS OF SURVEYING. [BOOK IV 

» 

Suppose a = 248230 feet, b = 212628 feet, and C = 103° 
19' 10". 

a. 248230 .log_ 5.394854 

&. 212628 .log- 5.327620 

G . . 103° 19' 10" . . . log sine . . . 9.988158 

ar. comp, of 2, diminished by 10 . . 1.698970 

20.409602 

Log of B.10. 

Log A. 10.409602 

Constant logarithm .... 9.326770 

Hence, . E =12.1" .\ . 1.082832. The sum of 

the three measured angles ought therefore to exceed 180°, 
by this amount. The angles being corrected, by subtract¬ 
ing 4.J" from each, the parts of the triangle may be com¬ 
puted, by regarding the sides as rectilineal. 

PLOTTING THE TRIANGULATION. 

/ ' ' ■ , '• 

37. The sides of the triangles being computed, after 
having made the necessary corrections, the work may then 
be plotted, as already explained, either by means of the 
circular protractor, or by the method of chords. 

THE CIRCULAR PROTRACTOR. 

38. This instrument consists of a brass circular limb 
(PI. 2, Fig. 4), of about six inches in diameter, with a 
movable index AB ) having a vernier at one extremity A, 
and a milled screw at the other extremity B, with a con¬ 
cealed cog-wheel that works with the cogs of the limb, and 
thus moves the index AB about the centre of the pro¬ 
tractor. At the centre of the protractor is a small circular 
glass plate, on which two lines are cut; the point of their 
intersection, is the exact centre of the instrument. The 
limb is generally divided to half degrees; the degrees are 
numbered from 0 to 360. 

At the 0 point, and at the opposite extremities of the 
diameter passing through that point, are small lines on the 
inner edge of the limb; the two extremities of the diam- 












OF PLOTTING. 


SEC. I.] 


193 


eter, perpendicular to this latter, are designated in the same 
way. 

Two angular pieces of brass, each having a small and 
sharp steel pin at its extremity, are fastened to the index, 
and revolve freely around the lines db and cd. The small 
screws, a, b , c, and d\ move them in the directions of the 
lines db, cd , for the purpose of bringing the steel pins ex¬ 
actly into the line which passes through the 0 of the in¬ 
dex and the centre of the protractor. 

To adjust them to their places, place the centre of the 
protractor over a marked point, and the 0 of the index to 
the 0 of the limb. Then mark the place of the index by 
the pins: after which, turn the index 180°, and see if the 
pins will mark the same points as before. If they do, the 
index is adjusted; if they do not, correct the error with the 
screws a, b 1 c, and d. 

TO LAY OFF AN ANGLE WITH THE PROTRACTOR. 

39. Let its centre be placed over the angular point, and 
the diameter passing through 0 and 180°, on the given line. 
Turn the screw that works the index, until the 0 of the 
vernier coincides with the division corresponding to the 
given angle; then let the angular brass pieces be turned 
down; the points dotted by the steel pins will show the 
direction of the required line. 

If this line does not pass through the angular point, 
the pins are out of place, and must be adjusted. 

FIRST METHOD OF PLOTTING. 

40. Suppose it were required to make the plan of the 
harbor on a scale of 450 yards to an inch. 

Divide the length of the base line AB, which we will 
suppose equal to 1140 yards, by 450, and the quotient 2.53 
will express the length which is to represent the base line 
on the paper (Bk. I., Art. 54.) 

Draw an indefinite line AB, to represent the base, and 
having chosen any point, as A, for the first station, lay ofi 
2.53 inches to B. The other extremity of the base line 
will thus be determined. 

13 


194 


ELEMENTS OF SURVEYING. [BOOK IT. 


Then, place the circular protractor at A, and lay off 
the angle BAE, and then the angle EAG. Next, place 
the protractor at B , and lay off the angles ABE and EBG. 
The intersection of the lines AE and BE will determine 
the station E. Let the protractor be then placed at this 
point, and all the angles of station E\ laid down. 

The point G, where EG intersects AG, and the point 
0, where EG intersects BG, will then be found. 

By placing the protractor at G and G, we can deter¬ 
mine the points D and F, when the place, on the paper, of 
all the stations will be known. 

To unite the work done with the compass, spread the 
compass-notes before you, and draw through A a line to 
represent the meridian. This line makes an angle of 12° 
with the course AE. 

Then, lay off from the scale the distances Aa, Ab, Aq, 
Ac, Ad, Ae, and at the several points erect perpendiculars 
to AE. Lay off on these perpendiculars the lengths of the 
offsets, and the curve traced through the points so deter¬ 
mined, will be the margin of the lake. 

At E, draw a parallel to the meridian through A, and 
lay down the course EH, which makes an angle of 50° with 
the meridian. Then, lay down the several distances to the 
offsets, and draw the offsets and lay off their lengths. Do 
the same for the course III, and all the compass-work will 
be plotted. 

The work done with the plane-table (Art. 28), is united 
to the work done with the theodolite, by simply placing 
the line AN on the paper of the plain-table, upon the line 
AN, drawn on the plot of the triangulation. 

SECOND METHOD OF PLOTTING-. 

41. Place the centre of the protractor near the centre 
of the paper, and draw a line through the points 0 and 
180°. This line will have the same position with the cir¬ 
cular protractor that the base line AB had with the limb 
of the theodolite. 


SEC. L] 


METHOD OF CHORDS. 


195 


Lay off then from tlie 0 point an arc equal to the direc¬ 
tion from A to B.\ also an arc equal to the direction AG, 
and through the centre point, and the points so determined, 
draw lines. Lay off in succession, in a similar manner, 
the directions taken at all the stations; and through the 
centre point, and the points so determined, draw lines, and 
designate each by the letters of the direction to which it 
corresponds. 

Now, since all the "lines drawn on the paper have the same 
position with the circular protractor, as the corresponding 
lines on the ground have with the limb of the theodolite, 
it follows that each direction will be parallel to its corres¬ 
ponding line upon the ground. 

Hence, any line may be drawn parallel to that passing 
through 0 and 180°, to represent the base line AB. Having 
drawn such a line, and marked a point for the station A , 
lay off the length of the base, and the extremity will be 
the station B. 

Through A and B, so determined, draw parallels re¬ 
spectively to the lines corresponding to the directions AB 
and BE\ and the point of intersection will determine station 
E. Through B and E draw parallels to the lines which 
correspond to the directions BO\ GB.\ and. their point of 
intersection will determine station 0. Through C and E 
draw lines parallel to the lines corresponding to the direc¬ 
tions GE and ED , and the point of intersection will de¬ 
termine D. In a similar manner we may determine the 
stations F and G. 


METHOD OF CHORDS. 

42. Let us first prove that the chord of a given arc is 
equal to the *sine of half the arc ivith double the radius. 

Let DAF be any given angle, 
and AH a line bisecting it. Let 
I)C be the chord of the arc CD , 
described with a given radius, 
and IIF parallel to CD , the sine 
of half the given angle, to a radius AF— 2AC. 




196 ELEMENTS OF SURVEYING. [BOOK IV. 

Since AF=2AG we have, from similar triangles, HF = 
2 KC, but DC=2KC, hence HF= CD. 

TO LAY OFF AN ANGLE. 

43. To avoid, as far as possible, 
the use of fractions, let us suppose 
the radius of the table of natural 
sines to be 1 ten , or 10 inches. 

Take from a scale 5 equal parts, 
with which as a radius, from the centre A , describe an 
arc CD. Take from the table the natural sine of half 
the arc, and remove the decimal point one place to the 
right; the result will express the sine of half the arc to the 
radius 10, or the chord of the arc to the radius 5. From 
the same scale, take this sine in the dividers, and from C, 
as a centre, describe an arc cutting CD in D; draw AD, 
and CAD will be the angle required. 

This is the most accurate of all the methods of laying 
off an angle, and it may also be applied advantageously to 
the second method of plotting, thus: 

Draw a fine straight line, generally 
in the direction of the meridian or of 
the base line of the survey; and also 
a line exactly perpendicular to it. From 
the point of intersection, as a centre, 
with a radius of 5 equal parts of the 
scale, describe the circumference of a 
circle cutting the straight lines in the points marked 0 
and 90°. 

To lay off an angle, as for instance, the angle 14° 29'. 
The half of it is 7° 14' 30", the natural sine of which is 
0.126005, or 1.26 to the radius of 10 inches. Set off from 
0 to b , as in the figure, this distance taken from the scale, 
and through the two points b, b , thus determined, draw a 
straight line. This line should pass through the centre, 
and will make with the line (0, 0) the angle 14° 29'; and 
any line on the paper drawn parallel to it, will make with 
the line (0, 0) the same angle. The further application is 
obvious. 


90 ° 








SEC. II.] 


MARITIME SURVEYING. 


197 


SECTION II. 

MARITIME 'SURVEYING. 

44. When, in connection with a trigonometrical survey 
on shore, a harbor is to be surveyed for the purpose of 
ascertaining the channels, their depth and width, the posi¬ 
tions of shoals, and the depth of water thereon, other 
means must be used, and other examinations made in ad¬ 
dition to those already referred to. 

Let buoys be anchored on the principal shoals and along 
the edges of the channel, and using any one of the lines 
already determined as a base, let the angles subtended by 
lines drawn from its extremities, to the buoys respectively, 
be measured with the theodolite. Then, there will be 
known in each triangle the base and angles at the base, 
from which the distances to the buoys are easily found ; 
and hence, their positions become known. 

Having made the soundings, and ascertained the exact 
depth of the water at each of the buoys, several points of 
the harbor are established, at which the precise depth of 
the water is known; and by increasing the number of the 
buoys, the depth of the water can be found at as many 
points as may be deemed necessary. 

45. If a person with a theodolite, or with any other in¬ 
strument adapted to the measurement of horizontal angles, 
be stationed at each extremity of the base line, it will not 
be necessary to establish buoys. A boat, provided with 
an anchor, a sounding line, and a signal flag, has only to 
throw its anchor, hoist its signal flag, and make the sound¬ 
ing, while the persons at the extremities of the base line 
measure the angles;—from these data, the precise place of 
the boat can be determined. 

46. There is another method of determining the places 
at which the soundings are made, that admits of great 


ELEMENTS OF SURVEYING. 


198 


[BOOK IV. 


despatch, and which, if the observations are made with 
care, affords results sufficiently accurate. 

Having established, trigonometrically, three points which 
can be seen from all parts of the harbor, and having pro¬ 
vided a sextant, let the sounding be made at any place in 
the harbor, and at the same time the three angles subtend¬ 
ed by lines drawn to the three fixed points, measured with 
the sextant. 

The problem, to find, from these data, the place of the 

boat at the time of the sounding, is the same as example 

6, page 62. 

* 

It is only necessary to measure two of the angles, but 
it is safest to measure the third also, as it affords a veri¬ 
fication of the work. 

The great rapidity with which angles can be measured 
with the sextant, by one skilled in its use, renders this a 
most expeditious method of sounding and surveying a 
harbor. 

The sextant is not described, nor are its uses explained 
in these Elements, because its construction combines many 
philosophical principles, with which the Surveyor cannot 
be supposed conversant. 

47. There is yet another method of finding the sound¬ 
ings, which, although not as accurate as those already ex¬ 
plained, will, nevertheless, afford results approximating 
nearly to the truth. It is this:—Let a boat be rowed uni¬ 
formly across the harbor, from one extremity to the other 
of any of the lines determined trigonometrically. Let 
soundings be made continually, and let the precise time of 
making each be carefully^ noted. Then, knowing the 
length of the entire line, the time spent in passing over it, 
as also the time of making each of the soundings, we can 
easily find the points of the line at which the several 
soundings were made; and hence, the depth of water at 
those points becomes known. 

48. If a person stationed on shore with a theodolite, takes 
the bearing of the boat, at every second or third sounding, 
determined by hoisting a flag, it will fix the positions of the 


SEC. II.] 


MARITIME SURVEYING. 


199 


soundings with great accuracy. Soundings may thus be 
made along any number of known lines, and a comparison 

of the depths found on different lines, at or near their 

points of intersection, will show with what degree of ac¬ 
curacy the work has been done. 

Sounding-lines should be made of strong cord, and di¬ 
vided into feet or fathoms, by different colored rags or 
other marks. The lead is shaped like 

the frustum of a cone, with the base 

B , hollowed out, to hold some grease. 

The land or mud of the bottom adheres 
to the grease, and thus shows the na¬ 
ture of the bottom, which should be en¬ 
tered in the field-book, and laid down 
upon the map. As the cord is liable 
to change its length, it should be com¬ 
pared from time to time with some 
standard. In tide-waters, the exact time 
of each sounding is to be noticed, and 
an assistant should note the height of the tide at regular in¬ 
tervals, upon a tide-guage. The tide-guage is permanently 
placed at some convenient point of the harbor, and its 0 
point is referred by means of a spirit-level, to some fixed 
bench-mark, on a level with mean low-water mark, to 
which all the soundings must be reduced. 

49. Having plotted the work done with the theodolite, 
as also the outline of the harbor traced with the compass, 
it remains to delineate the bottom of the harbor; and this 
is done by means of horizontal curves, which have already 
been used to represent broken or undulating ground. 

Let the plane of reference Ke taken through low-water 
mark, or to coincide with the surface of the water at low 
tide. The accuracy with which the bottom of the harbor 
is to be delineated, will guide us in fixing the distance be¬ 
tween the horizontal planes of section. 

The first horizontal plane should be passed at a dis¬ 
tance below the shallowest point that has been sounded, 
equal to the number of feet fixed upon for the distance 
between the planes of section; and the curve, in which it 



200 


ELEMENTS OF SURVEYING. 


[BOOK IV. 


intersects the bottom of the harbor determined as in Book 
III. Sec. II. And similarly, for the other horizontal planes 
of section. 

Haying thus delineated the bottom of the harbor, and 
noted on the map the distance of each intersecting plane 
below the plane of reference, let such lines be drawn as 
will indicate the channels, shoals, sunken rocks, and direc¬ 
tion of the current. 

In the example given in plate 6, soundings have been 
made in three directions from the sand-bar in the harbor, 
and also from the rocky shore across to the light-house. 


BOOK V. 

OF NAVIGATION. 


SECTION I. 

DEFINITIONS. 

/ 

1. We have given, in the preceding parts of this work, 
various applications of Plane Trigonometry. We propose, 
in this Book to explain the best methods of determining 
the place of a ship at sea. This application of Trigonom¬ 
etry constitutes the science and art of Navigation. 

2. There are two methods of determining the place of 
a ship at sea. 

1st. When a ship departs on her voyage, if we note 
her courses and the distance sailed, we may, at any time, 
by means of Plane Trigonometry, determine her place, very 
nearly. 

2d. By means of observations on the heavenly bodies, 
and the aid of Spherical Trigonometry, we may determine 
with great accuracy, the place of the ship. This method 
is called Nautical Astronomy. 

The first part of Navigation, viz., the cases which can 
be solved without the aid of observations on the heavenly 
bodies, will be alone treated of. 

3. The earth is nearly spherical. For the purposes of 
Navigation it may be considered as perfectly so. It re¬ 
volves round one of its diameters, called the axis ) in about 
twenty-four hours. 

4. The great circle, whose poles are the extremities of 
the axis, is called the equator. The poles of the equator 



202 


ELEMENTS OF SURVEYING. [BOOK V 


are called tlie poles of tlie earth—one is called the north 
pole, and the other the south pole. 

5. The circumference of every great circle which passes 
through the poles, cuts the equator at right angles, and is 
a meridian circle. Every place on the surface of the earth 
has its own meridian ; but for the purposes of Geography 
and Navigation, all the meridians are reckoned from a par¬ 
ticular meridian, which is called the first meridian. The 
English have fixed on the meridian of the Greenwich Ob- 
servatory, for the first meridian. 

0. The longitude of any place is the arc of the equator, 
intercepted between the meridian of that place and the first 
meridian, and is east or west, according as the place lies 
east or west of the first meridian. 

7. The difference of longitude of two places is the arc of 
the equator included between their meridians; this arc is 
equal to the difference of longitudes when they are of the 
same name, and to the sum of the longitudes, when they 
are of different names. 

8. The latitude of a place is its distance from the equator, 
measured on the meridian of the place, and is north or south 
according as the place lies north or south of the equator. 

9. The small circles drawn parallel to the equator, are 
called parallels of latitude. The arc of any meridian inter¬ 
cepted between the parallels passing through any two 
places, measures the difference of latitude of those places; 
this difference is found by subtracting the less latitude from 
the greater, when the latitudes are of the same name, and 
by adding them when they are of different names. 

10. The sensible horizon of any place is an imaginary 
plane, supposed to touch the earth at that place, and to be 
extended indefinitely. 

A plane passing through the centre of the earth, and 
parallel to the sensible horizon, is called the rational horizon. 

The north and south line, is the intersection of the 
plane of the meridian circle with the sensible horizon, and 
the line which is drawn perpendicular to this, is called the 
east and west line. 


SEC. I] 


NAVIGATION. 


203 


11. The course of a sliip, at any point, is the angle which 
her track or keel makes with the meridian. So long as the 
course is unchanged, the ship would sail in a straight line, 
if the meridians were truly parallel; but as the meridians 
bend constantly toward the pole, the direction of her path is 
continually changing, and she moves in a curve called the 
rhumb line. The course of a ship is indicated by the mari¬ 
ner’s compass. 

12. The marin¬ 
er’s compass consists 
of a circular card, 
whose circumfer¬ 
ence is divided into 

-two equal 
parts called points ; 
each point being 
subdivided into four 
parts, called quar¬ 
ter points. 

To the under 
side of this card a 
slender bar of mag¬ 
netized steel, called 
a needle , is permanently attached. The direction of the 
needle corresponds to the diameter IN’S. The diameter EW, 
at right angles to NS, is intended to indicate the east and 
west points. The points of the compass are thus read: be¬ 
ginning at the north point, and going east, we say, north 
and by east , north north east, north east and by north, 
north east; and so on, round the compass, as indicated by 
the letters. 

The card being permitted to turn freely on the pin, on 
which it is poised, as a centre, the line NS will always 
indicate the true magnetic meridian, but this, as we have 
seen in (Bk. II., Sec. 7-14), is not the true meridian, and 
hence, the variation must always be allowed for. 

On the interior of the compass box, in which the card 
swings, are two marks a and b ) which lie in a line passing 
through the centre of the card, and the compass box is so 










204 


ELEMENTS OF SURVEYING. 


[BOOK V. 


placed that this line shall be parallel to the keel of the 
ship. Consequently, if b be placed towards the bow of the 
vessel, the point which it marks on the card will show the 
compass course, for the line NS is always on the magnetic 
meridian, and EW is east and west. The course is gene¬ 
rally read to quarter points, and as a quadrant contains 
eight points, each point is equal to 90° -f- 8 = 11° 15'; and 
a quarter point = 11° 15 / -r-4=2° 48' 45". The table of 
Rhumbs, after the Traverse Table, shows the degrees in 
each course, to quarter points. 

13. A ship’s rate of sailing is determined by • means of 
an instrument, called the log , and an attached line called 
the log line. The log is a piece of wood in the form of a 
sector' of a circle, the rim of which is loaded with lead, so 
that when it is heaved into the sea it assumes a vertical 
position. The log line is so attached as to hold the log 
square against the water, that it may not be drawn along 
after the ship as the line unwinds from the reel, by the 
ship’s forward motion. 

The time in which the log line unwinds from the reel, 
is noted by a sand-glass, through which the sand passes in 
half a minute; that is, in the one hundred and twentieth part 
of an hour. 

For convenience, the log line is divided into equal parts, 
marked by knots ) and each part is equal to the one hun¬ 
dred and twentieth part of a nautical or geographical 
mile 45 '. 

Now, since half a minute is the one hundred and twen¬ 
tieth part of an hour, and each knot indicates the one hun¬ 
dred and twentieth part of a mile, it follows that the num¬ 
ber of knots reeled off while the half minute glass runs out, 
will indicate the rate of the ship’s sailing per hour. 


* A geographical mile is one minute, or one-sixtieth of a degree, measured on 
the equator. Taking the diameter at 7916 English miles, the geographical mile 
.will be about 6079 feet; that is, one-sixth greater than the English mile which 
is 5280 feet. 




sec. in 


PLANE SAILING. 


205 


SECTION II. 

* 

OF PLANE SAILING. 

14. Let the diagram 
EPQ represent a por¬ 
tion of the earth’s sur¬ 
face, P the pole, and 
EQ the equator. Let 
AB be any rhumb line, 
or track described by 
a ship in sailing from 
A to B. 

Conceive the path of the ship to be divided into very 
small parts, and through the points of division draw meri¬ 
dians, and also the parallels of latitude b'b , c'c, d'd, e'e, and 
B'B\ a series of triangles will thus be formed, but so small 
that each may be considered as a plane triangle. 

In these triangles, the sum of the bases 
Ah' + be! -f cd! + de' + ef— AB', 

which is equal to the difference of latitude between the 
points A and B. Also, 

b'b + e'e + d'd + e'e + fB = BB\ 

which is equal to the distance that the ship has departed 
from the meridian AB'P , and is called the departure in 
sailing from A to B. 

Therefore, the distance sailed, the dif¬ 
ference of latitude made, and the departure , 
may be represented by the hypothenuse, 
the base and perpendicular of a right- 
angled triangle, of which the angle op¬ 
posite the departure is the course. 

When any of the four parts above- 
named are given, the other two can be 
determined. This method of determining 
the place of a ship reduces all the elements to the parts 
of a plane triangle, and hence is called plane sailing. 











206 


ELEMENTS OF SURVEYING. 


[BOOK V. 


EXAMPLES. 


1. A ship from latitude 47° 30' 1ST. has sailed S. W. by 
S. 98 miles. What latitude is she in, and what departure 
has she made ? 


Let 0 be the place sailed from, CB 
the meridian, and BOA the course, which 
we find from the table of rhumbs to be 
equal to 33° 45'; then AO will be the dis¬ 
tance sailed, equal to 98 miles. Also, AB 
will be the departure, and CB the differ¬ 
ence of latitude. 

Then by the formulas for the solution 
of right angled triangles, 



As radius ar. c. 0.000000 
: cos C 33° 45' 9.919846 

::AO 98 1.991226 


CB 


81.48 1.911072 


As radius ar. c. 0.000000 

: sin C 33° 45' 9.744739 

: : CA 98 1.991226 


: AB 54.45 


1.735965 


Latitude left 47° 30' N. 

Dif. lat. = 81.48 miles = 81.48 minutes = 1° 22' S. 


In latitude 46° 08'. 


Departure, 54.45 miles. 

2. A ship sails 24 hours on a direct course, from lat¬ 
itude 38° 32' 1ST. till she arrives at latitude 36° 56' 1ST. 
The course is between S. and E. and the rate 5J miles an 
hour. Required the course, distance, and departure. 

Lat. left 38° 32' 1ST. 24 X 5J = 132 miles = distance. 
In lat. 36° 56' 


Diff. 1° 36' = 96 miles. 


As dist. 132 ar. c.* 7.879426 
: diff. lat. 96 1.982271 

: : radius 10.000000 


As radius ar. c. 0.000000 
: dist. 132 2.120574 

:: sin course 43° 20' 9.836477 


: dep. 


: cos course 43° 20' 9.861697 


90.58 1.957051 





















SEC. Ill] TRAVERSE SAILING. 207 

Hence, the course is S. 43° 20' E., and the departure 
90.58 miles east. 

3. A ship sails from latitude 3° 52' S. to latitude 4° 30' 
K, the course being N. W. by W. £W.: required the dist¬ 
ance and departure. 

Ans. Dist. 1065 miles; dep. 939.2 miles W. 

4. Two points are under the same meridian, one in lat¬ 
itude 52° 30' 1ST., the other in latitude 47° 10' 1ST. A ship 
from the southern place sails due east, at the rate of 9 
miles an hour, and two days after meets a sloop that had 
sailed from the other : required the sloop’s direct course, and 
distance run. 

Ans. Course S. 53° 28' E.; dist. 537.6 miles. 

5. If a ship from latitude 48° 27' S., sail S. W. by W. 

7 miles an hour, in what time will she reach the parallel 
of 50° south? Ans. 23.914 hours. 


SECTION III. 

OF TRAVERSE SAILING. 

15. When a ship, in going from one place to another, 
sails on different courses, it is called Traverse Sailing. The 
determination of the distance and course, from the place of 
departure to the place of termination, is called compounding 
or working the traverse. This is done by the aid of the 
u Traverse Table,” which has already been explained, and 
the method of working the traverse, is in all respects simi¬ 
lar to that adopted in the Prob. of Art. 34, page 123. 

EXAMPLES. 

* 

1. A ship from Cape Clear, in lat. 51° 25' 1ST., sails, 1st, 
S. S. E. i E. 16 miles; 2d, E. S. E. 23 miles; 3d. S. W. 
by W. i W. 36 miles; 4th, W. f N. 12 miles; 5th, S. E. 
by E. \ E. 41 miles : required the distance run, the direct 
course, and the latitude. 



208 


ELEMENTS OF SURVEYING. 


[BOOK V 


We first form the table 
below, in which we enter 
the courses, from the table 
of rhumbs, omitting the 
seconds, and then enter 
the latitudes and depart¬ 
ures, taken from the tra¬ 
verse table, to the nearest 
quarter degree. Thus, in 
taking the latitude and 
departure for 25° 18' we 
take for 25J°. The dif¬ 
ference of latitudes gives 
the line AG , and the dif¬ 
ference of departures the 
line GF. 



TRAVERSE TABLE. 


Courses. 

Dist’s. 

Diff. of Latitude. 

Departure. 

No 


Angle. 


N. 

s. 

E. 

w. 

1 

S. S.E.IB. . . 

25° 18' 

16 


1447 

6.83 


2 

E. S. E. 

—I 

o 

CO 

o 

23 


8.80 

21.55 


3 

S. W. by W. i W. 

61° 52' 

36 


17.04 


31.71 

4 

W.fN . 

81° 33' 

12 

1.77 



11.87 

5 

S. E. by E. i E. . 

59° 03' 

41 


21.12 

35.14 






1.77 

61.43 

63.22 

43.58 






1.77 

43.58 



• 



Diff. 

59.66 

19.64 



Latitude left 51° 25' N. 

Difference of latitude 59.66 miles = 1° 00' S. 




In latitude 50° 25' 1ST. 






































SEC. III.] 


TRAVERSE SAILING. 


209 


Then, by formulas for the solution of right-angled tri¬ 
angles, we have, 


As sin course ar. c. .504995 


As A 6r, diff. lat. ar. c. 8.224317 
: departure 19.64 1.293141 
: : radius, 10.000000 

: tang course 18° 13' 9.517458 


: radius 10.000000 

:: departure 19.64 1.293141 

: distance 62.83 1.798136 


Therefore the direct course is S. 18° 13' E., and the 
distance 62.83 miles. 


OF PLOTTING. 

16. There is yet another method of finding the direct 
course and distance, much practiced by seamen, although 
it does not afford. a high degree of accuracy. It is a 
method by plotting, which requires the use of a mariner’s 
scale and a pair of dividers. 

One of the scales marked on the mariner’s scale, is a 
scale of chords, commonly called a scale of rhumbs, being 
divided to every quarter point of the compass; and there 
is also a second scale of chords divided to degrees. Both 
of these scales are constructed in reference to the same 
common radius, so that the chords on the scale of rhumbs 
correspond to those on the scale of marked chords. The 
manner of using the scales will appear in plotting the last 
example. 

To construct this traverse, describe a circle with a radius 
equal to the chord of 60° and draw the meridian NS. 
Then take from the line of rhumbs the chord of the first 
course points, and apply it from S to 1, to the right of 
NS, since the course is southeasterly, and draw A1 ; take, 
in like manner, the chord of the second course, 6 points, 
from A to 2, and lay it off also to the right of the meri¬ 
dian line. Apply the chord of the third course, 5J points, 
from S to 3, to the left of the meridian; the fourth course, 
7} points from N to 4, to the left of NS, this course be¬ 
ing northwesterly; and, lastly, apply the chord of the fifth 
course, 5-J points, from S to 5, to the right of NS, and 
join all the lines as in the figure. 

14 







210 ELEMENTS OF SURVEYING-. [BOOK V. 

In tlie direction Al, lay off the distance AH = 16 miles 
from a scale of equal parts, and through the extremity II, 
draw IIC parallel to A2, and lay off HQ— 23 miles. Draw 
CD parallel to A3, and lay off CD — 36 miles; then draw 
DE parallel to A4, and lay off 12 miles; and lastly, draw 
EF parallel to Ad, and lay off 41 miles, and F will be the 
place of the ship. Hence, we conclude that AF is the dist- 
ance made good, and CAF is the course. 

Applying, then, the distance AF to the scale of equal 
parts, we find it equal to 62J miles; and applying the 
chord Sa to the scale of chords, we find the course CAF 
= 18i°. 

2. A ship sails from a place in latitude 24° 32' N., and 
runs the following courses and distances, viz., 1st, S. W. 
by W. dist. 45 miles ; 2d, E. S. E. dist. 50 miles ; 3d, S. 
W. dist. 30 miles; 4tli, S. E. by E. dist. 60 miles ; 5th, S. 
W. by S. 4 W. dist. 63 miles : required her latitude, and 
the direct course and distance from the place left to the 
place arrived at, and the construction of the traverse. 

j Eat. 22° 3' N., course S. 

I Dist. 149.2 miles. 

3. A ship from lat. 28° 32' H. has run the following 
courses, viz., 1st, N. W. by N. 20 miles; 2d, S. W. 40 miles; 
3d, 1ST. E. by E. 60 miles; 4th, S. E. 55 miles ; 5th, W. 
by S. 41 miles; 6th, E. N. E. 66 miles: required her lat¬ 
itude, the distance made good, and the direct course, also 
the construction of the traverse. 

Ans. Dist. 70.2 miles, course E. 

4. A ship from lat. 41° 12' K sails S. W. by W. 21 
miles; S. W. 4 S. 31 miles ; W. S. W. i S. 16 miles: S. 
f E. 18 miles; S. W. 4 W. 14 miles; then W. 4 K 30 
miles: required the latitude, the direct course, and the 
distance. 

An S i^at. 40° 05', course S. 52° 49' W. 

1 Dist. 111.7 miles. 

5. A ship runs the following courses, viz.: 

1st, S. E. 40 miles; 2d, K E. 28 miles; 3d, S W. by 
W. 52 miles; 4th, K W. by W. 30 miles; 5th, S. S. E. 


SEC. IV.] 


PARALLEL SAILING. 


211 


36 miles; 6th, S. E. by E. 58 miles: required the direct 
course, and distance made good. 

A ns j Direct course S. 25° 59' E., or S. S. E. \ E., nearly. 

(Distance 95.87 miles. 

6. A ship sails, 1st, 1ST. W. by W. % W. 40 miles; 2d 
N. W. by {■ N., 41 miles ; 3d, N. by E. 16.1 miles ; and 
4tli, IN. E. i E. 32.5 miles : required the distance made, 
and the direct course. 

Ans. Course, 21° 54' West of North. Dist. 94.6 miles. 

These examples will, j^rhaps, suffice to illustrate the 
principles of plane sailing. 

The longitude, made on any course, cannot be deter¬ 
mined by these methods, for this being the arc of the 
equator intercepted between two meridian , cannot be found 
under the supposition that the meridians are parallel. 

The most simple case of finding the difference of lon¬ 
gitude is when the ship sails due east or due west: this is 
called Parallel Sailing. 


SECTION IV. 

PARALLEL SAILING. 

17. The entire theory of parallel sailing is comprehend¬ 
ed in the following proposition, viz.: 

The cosine of the latitude of the parallel , is to radius , as 
the distance run to the difference of longitude. 

Let IQH represent the equa¬ 
tor, and FDN any parallel of 
latitude: then, Cl will be the 
radius of the equator, and EF 
the radius of the parallel. 

Suppose FD to be the dis¬ 
tance sailed, then the differ¬ 
ence of longitude will be meas¬ 
ured by IQ, the arc intercept¬ 
ed on the equator. Then, 


P 









212 


ELEMENTS OF SURVEYING. [BOOK V 


since similar arcs are to each 
other as their radii (Geom., 

Bk. V., Prop. 14), we have, 

EF : Cl : : dist. FB : 
diff. long. IQ. 

But EF is the sine of PF\ 
or cosine of FI, the latitude: 
and Cl is the radius of the 
sphere: hence, 

cos lat. : R : : distance : 
diff. longitude. 

18. If we denote by D the distance between any two 
meridians, measured on the parallel whose latitude is L ; 
and by B' the distance between the same meridians meas¬ 
ured on the parallel whose latitude is L the arcs are 
similar, and we shall have (Geom., Bk. V., Prop. 14), 

cos L : B :: cos II : B’, 
that is, cos L : cos L' : : B : B'. 

9 

Hence, when the longitude made on different parallels is the 
same , the distances sailed are proportional to the cosines of the 
parallels of latitude. 

19. By referring to Th. Y., Bk. I., we see that in any 
right-angled triangle 

R : cos angle at base : : hyp. : base, 
or cos E : R : : EC : EG; 
and by comparing this with the propor¬ 
tion, 

cos lat. : R : : dist. : diff. long; 
we see, that if in a right-angled* triangle 
the angle at the base be made equal to 
the latitude of the parallel, and the base 
to the distance run ; then, the hypothenuse will represent 
the difference of longitude. 

It follows therefore, that any problem in parallel sail¬ 
ing, may be solved as a simple case of plane sailing. For, 
if we regard the latitude as the course, the distance run 
as the base, the difference of longitude will be the hypo¬ 
thenuse of the corresponding right-angled triangle. 



P 












SEC. IV.] 


PARALLEL SAILING. 


218 


EXAMPLES. 


1. A ship from latitude 53° 56 1ST., longitude 10° 18' 
E., has sailed due west, 236 miles : required her present 
longitude. 


By the rule 
As cos lat. 53° 56' 
: radius 

: : distance 236 . 

: diff. long. 400.8 
Long, left 


ar. c. . .230087 

. 10.000000 

. 2.372912 


2.602999 


10° 18' E. 


400 


Diff. long. = degrees = 6° 40' W. 


Long. . . , 3° 38' E. 


2. If a ship sails E. 126 miles from the North Cape, 
in lat. 71° 10' N., and then due N., till she reaches lat. 
73° 26' N.; how far must she sail W. to reach the meri¬ 
dian of the North Cape? 

Here the ship sails on two parallels of latitude, first on 
the parallel of 71° 10', and then on the parallel of 73° 26', 
and makes the same difference of longitude on each parallel. 

Hence, by Art. 18, 

As cos lat. 71° 10' arith. comp. 0.491044 
: distance 126 . . 2.100371 

: : cos lat. 73° 26' . . ' 9.455044 

: distance 111.3 . . 2.046459 


3. A ship in latitude 32° N. sails due E. till her dif¬ 

ference of longitude is 384 miles: required the distance 
run. Ans. 325.6 miles. 

4. If two ships in latitude 44° 30' N., distant from 
each other 216 miles, should both sail directly S. till their 
distance is 256 miles, what latitude would they arrive at? 

Ans. 32° 17' N. 









214 


NAVIGATION. 


[BOOK V. 


5. Two ships in the parallel of 47° 54' 1ST., have 9° 85' 
difference of longitude, and they both sail directly S., a 
distance of 836 miles: required their distance from each 
other at the parallel left, and at that reached. 

Ans. 385.5 miles, and 479.9 miles. 


SECTION V. 

MIDDLE LATITUDE SAILING. 

20. Having seen how the longitude which a ship makes 
when sailing on a parallel of latitude may be determined, 
we come now to examine the more general problem, viz., 
to find the longitude which a ship makes when sailing 
upon any oblique rhumb. 

There are two methods of solving this problem, the one 
by what is called middle latitude sailing , and the other by 
Mercator's sailing. The first of these methods is confined 
in its application, and is moreover somewhat inaccurate 
even where applicable; the second is perfectly general, and 
rigorously true; but still there are cases in which it is advi¬ 
sable to employ the method of middle latitude sailing, in 
preference to that of Mercator’s sailing. It is, therefore, 
proper that middle latitude sailing should be explained, 
especially since, by means of a correction to be hereafter 
noticed, the usual inaccuracy of this method may be 
rectified. 

Middle latitude sail¬ 
ing proceeds on the 
supposition that the de¬ 
parture or sum of all 
the meridional distan¬ 
ces, b'b , c'c : d'd, &c.j 
from 0 to T, is equal 
to the distance M'M 
between the meridians 
passing through 0 and T\ measured on the parallel of lati¬ 
tude equally distant from 0 and T. 



Q 










SEC. V.] MIDDLE LATITUDE SAILING. 215 

The middle latitude is half the sum of the two extreme 
latitudes, if they are both of the same name, and half 
their difference, if they are of contrary names. 

The supposition above becomes very inaccurate when the 
course is small, and the distance run great; for it is plain that 
the middle latitude distance will receive a much greater acces¬ 
sion than the departure, if the track OT cuts the successive 
meridians at a very small angle. 

The principal approaches nearer to accuracy as the angle 
0 of the course increases, because then as but little ad¬ 
vance is made in latitude, the several component depart¬ 
ures lie more in the immediate vicinity of the parallel M'M. 
But still, in very, high latitudes, a small advance in lat¬ 
itude makes a considerable difference in meridional dist¬ 
ance ; hence, this principle is not to be used in such lat¬ 
itudes, if much accuracy is required. 

By means, however, of a small table of corrections, con¬ 
structed by Mr. Workman , the imperfections of the middle 
latitude method may be removed, and the results of it ren¬ 
dered in all cases accurate. This table we have given at 
the end of this work. 

21. The rules for middle latitude sailing may be thus 
deduced. 

We have seen, in the first case of plane 
sailing, that if a ship sails on an oblique 
rhumb from 0 to T, that the hypothenuse 
OT will represent the distance; OT' the 
difference of latitude, and T'T, the depart¬ 
ure. blow, by the present hypothesis, 
the departure T'T is equal to the middle 
parallel of latitude between the meridians 
of the places sailed from and arrived at: 
so that the difference of longitude of these two places is the 
game as if the ship had sailed the distance T'T on the mid¬ 
dle parallel of latitude. The determination of the differ¬ 
ence of longitude is, therefore, reduced to the case of par¬ 
allel sailing: for, T'T now representing the distance on the 
parallel, if the angle T'TO' be made equal to the latitude of 


O' 






216 


NAVIGATION. 


[BOOK V. 


that parallel, we shall have, by the last case, the difference 
of longitude represented by the hjpothenuse O'T. We 
therefore have the following theorems: 

I. In the triangle O'TT', 

cos O'TT' : TV :: R : TO ; 

that is, 

cos mid. lat. : departure : : R : diff. longitude. 

II. In the triangle O' TO 

sin O' : OT : : sin 0 : O'T ; 
that is, since sin O' = cos O'TT' 

cos mid. lat. : distance :: sin. course : diff. longitude. 

III. In the triangle OTT', we have 

R : tangent 0 : : OT' : TT '; 

comparing this with the first proportion, and observing 
that the extremes of this are the means of that, we have 

OT' : O'T : : cos O'TT' : tang 0; 

that is, 

diff. lat. : diff. long. : : cos mid. lat. : tang course. 

These three propositions comprise the theory of mid¬ 
dle latitude sailing; and when to the middle latitude sail¬ 
ing, the proper correction, taken from Mr. Workman’s table, 
is applied, these theorems will be rendered accurate. 

In the table of pages 93 and 94, the middle latitude is 
to be found in the first column to the left. Then, along 
the horizontal line, and under the given difference of lat¬ 
itude, is inserted the proper correction to be added to the 
middle latitude to obtain the latitude in which the meri¬ 
dian distance is accurately equal to the departure. Thus, 
if the middle latitude be 37°, and the difference of latitude 
18°, the correction will be found on page 94, and is equal 
to 0° 40'. 


7 

EXAMPLES. 

« 

1. A ship, in latitude 51° 18' 1ST., longitude 22° 6' W., 
is bound to a place in the S. E. quarter, 1024 miles dis¬ 
tant, and in lat. 37° N.: what is her direct course and dis- 


SEC. V.] MIDDLE LATITUDE SAILING. 


217 


tance, as also the difference of longitude between the two 
places ? 

Lat. from 51° 18' 1ST. ) ^ l 

Sum oi latitudes . 


Lat. to 87° 0 N. 


Mid. lat. 


88° 18' 
44° 9' 


Diff. lat. 14° 18 = 858 miles. 
As distance 1024 6.989700 

: radius 10.000000 

: : diff. lat. 858 2.933487 


: cos course 33° 5' 9.923187 


Cos mid lat 44° 9' ar c 0.144167 
: tang course 33° 5' 9.813899 
: : diff. lat. 858 2.933487 


: diff. long. 779 


2.891553 


In this operation the middle latitude has not been cor¬ 
rected, so that the difference of longitude here determined 
is not without error. To find the proper correction, look 
for the given middle latitude, viz., 44° 9', in the table of 
corrections, the nearest to which we find to be 45° ; against 
this and under 14° diff. of lat. we find 27'; and also, under 
15° we find 31', the difference between the two being 4'; 
hence, corresponding to 14° 18' the correction will be about 
28'. Hence, the corrected middle latitude is 44° 37', 
therefore, 

Cos corrected mid. lat. 44° 37' ar. comp. 0.147629 
: tang, course 33° 5' . . 9.813899 

: : diff. lat. 858 . . . 2.933487 


: diff. long 


785.3 . . 2.895015 


therefore, the error in the former result is about 6J miles. 

2. A ship sails in the K. W. quarter, 248 miles, till her 
departure is 135 miles, and her difference of longitude 310 
miles: required her course, the latitude left, and the lat¬ 
itude come to. 

a \ Course 1ST. 32° 59' W.; 
ns 'j Lat. left 62° 27' K; lat. in 65° 55' K 

3. A ship, from latitude 37° 1ST., longitude 9° 2' W., 
naving sailed between the 1ST. and W., 1027 miles, reckons 
that she has made 564 miles of departure : what was her 
direct course, and the latitude and longitude reached ? 

a (Course N. 33° 19' W., or K W. nearly; 
n5 ’ 1 Lat. 51° 18' K; long. 22° 8' W. 










218 


NAVIGATION. 


[BOOK V. 


t 


4. Required the course and distance from the east point 
of St. Michael’s, lat. 37° 48' K, long. 25° 13' W., to the 
Start Point, lat. 50° 13' If., long. 3° 38' W. ; the middle 
latitude being corrected by Workman’s table. 

Ans. Course 1ST. 51° 11' E.; disk 1189 miles. 

Mercator’s sailing. 

22. It has already been observed, that when a ship 
sails on an oblique rhumb, the departure, the difference of 
latitude, and the distance run, are truly represented by 
the sides of a right-angled triangle. 

Thus, if a ship sails from A to L>, the 
departure B'B will represent the sum of 
all the very small meridian distances, 
or elementary departures, b'b , p"p, &c.; 
the difference of latitude AB' will re¬ 
present, in like manner, the small dif¬ 
ferences of latitude Ah ', b'p\ &c.; and 
the hypotlienuse AB : will express the 
sum of the distances corresponding to 
these Several differences of latitude 
and departure. Each of these elements is supposed to be 
taken so small, as to form on the surface of the sphere a 
series of triangles, differing insensibly from plane triangles. 

Let ABB' be a triangle, in which the angle A repre¬ 
sents the course, AB' the difference of latitude, B'B the 
departure, and AB the distance run. Produce the side 
AB to C\ until CC shall be equal to the difference of 
longitude of the two extremities of the course : then, for 
the sake of distinction, we call 

AB' = the proper difference of latitude, 

AC' — the meridional difference of latitude, 
and we are now to explain the manner of constructing a 
table, called a table of meridional parts, which will furnish 
the meridional differences of latitude when the proper differ¬ 
ences are known. 

Let Ab’b represent one of the elementary triangles; b'b 
will then be one of the elements of departure; and Ab' 
the corresponding difference of latitude. Now, as b'b is a 
small arc of a parallel of latitude, it is to a portion of the 









SEC. V.] 


MERCATOR’S SAILING 


219 


# # 

equator containing an equal number of degrees, as tlie co¬ 
sine of its latitude is to radius (Art. 17). This similar 
portion of the equator, is the difference of longitude be¬ 
tween b' and b. 

Suppose, now, that Ah' is prolonged to p\ making p'p 
equal to the difference of longitude between b and b' : then 

bb' : pp' : : cos lat. b'b : E (Art. 17.) 

But, bj similar triangles, we have 

bb' : pp 1 : : Ab' : Ap ', 
and consequently, 

proper lat. Ab' : mer. diff. of lat. Ap' : : cos lat. bb' : 1. 

Denoting the proper difference of latitude by <7, the 
meridional difference of latitude by B, the latitude of b'b 
by Z, and the radius by 1, which is, indeed, the radius of 
the table of natural sines, we shall have 

d : B : : cos Z : 1, 

which gives 

B — d secant Z, since - i = sec. Z. 

cos Z 

If then, we know the latitude Z of the beginning of a 
course, and the proper difference of latitude d of the ex¬ 
tremity of the course, we can easily find the meridional 
latitude B corresponding to that course. 

The determination of AC' which represents the meri¬ 
dional difference of latitude, involves the determination of 
all the elementary parts, on which it depends. If d be 
taken equal to l', we shall have from the equation above 
B—l' sec. Z, or B — sec. 1, 

it being understood that Z expresses minutes or geographi¬ 
cal miles. 

From this equation, the value of B , corresponding to 
every minute of Z, from the equator to the pole, may be 
calculated ; and from the continued addition of these, there 
may be obtained, in succession, the meridional parts cor¬ 
responding to 1', 2', 3 ', 4 ', &c., of proper latitude,, and when 
registered in a table, they form a table of meridional parts, 
given in all books on Navigation. 

The following may serve as a specimen of the manner 
in which such a table may be constructed, and, indeed, of 
the manner in which the first table of meridional parts was 



220 


NAVIGATION. 


[BOOK V 


actually formed by Mr. Wright, the jmoposer of this valu¬ 
able method. 

Mer. pts. of 1' - nat. sec. 1'. 

Mer. pts. of 2' = nat. sec. 1' + nat. sec. 2'. 

Mer. pts. of 3' = nat. sec. V + nat. sec. 2' + nat. sec. 3'. 

Mer. pts. of 4' = nat. sec. 1' + nat. sec. 2' + nat. sec. 3' + &c. 

Hence, by means of a table of natural secants we have 

Nat. Secs. Mer. Pts. 

Mer. pts. of V = . 1.000000 = 1.0000000 

Mer. pts. of 2' = 1.0000000 + 1.0000000 - 2.0000002 

Mer. pts. of 3' = 2.0000002 + 1.0000004 = 3.0000006 

Mer. pts. of 4' = 3.0000006 + 1.0000007 = 4.0000013, &c.* 

There are other methods of construction, but this is the 
most simple and obvious. The meridional parts thus de¬ 
termined, are all expressed in geographical miles, because 
in the general expression 

D= V sec. Z, 

1' is a geographical mile. 

23. Having thus formed the table of meridional parts, 
if we find from it, the meridional parts corresponding to 

the latitudes of the place left and the place arrived at, 

their difference will be the meridional difference of lat¬ 
itude, or the line AC' in the diagram. The difference of 
longitude denoted by C'C may then be found by the fol¬ 
lowing proportion. 

I. As radius is to the tangent of the course , so is the meri¬ 
dional difference of latitude to the difference of longitude. 

But if the departure be given instead of the course, then, 

II. As the proper difference of latitude is to the departure , 
so is the meridional difference of latitude to the longitude. 

Other proportions may also be deduced from the diagram. 

EXAMPLES. 

As an example of Mercator’s or rather Wright’s, sailing, 
let us take the following: 

1. Required the course and distance from the east point 
of St. Michael’s to the Start point: the latitudes being 37° 
48' N., and 50° 13' H., and the longitudes 25° 13' W., and 
3° 38' W. 


SEC. V.] 


MERCATOR’S CHART. 


221 


Start Point, lat. 50° 13' N. Mer. pts. 3495 

St. Michael’s, lat. 37° 48' 1ST. Mer. pts. 2453 


Proper difference of lat. 12° 25' 

60 

Diff. in miles 745 


Mer. diff. 1042 

Diff. of long. 21° 35' 
60 


Diff. in miles 1295 


,Now, let ns suppose that we have 
sailed from A to B: we shall then 
know AB' equal proper diff. lat. = 745 
miles; A C' = meridional diff. of lat. = 
1042; and G'C=i\\e difference of lon¬ 
gitude equal to 1295 miles. It is re¬ 
quired to find the course B'AB 1 and the 
distance AB. 


C' C 



For the Course. . For the Distance. 


As AC' 

1042 6.982132 

As cos A 

51° 11' 

0.202850 

: radius 

10.000000 

: AB' 

745 

2.872156 

: : CC 

1295 3.112270 

:: radius 


10.000000 

tang. A 51° 11' E. 10.094402 

: AB 

1189 

3.075006 


2. A ship sails from latitude 37° 1ST. longitude 22° 56' 
W., on the course N. 33° 19' E.: till she arrives at 51° 
18' II.: required the distance sailed, and the longitude ar¬ 
rived at. Ans. Dis. 1027 miles; long. 9° 45' W. 


mercator’s chart. 

24. Mercator’s Chart is a Map constructed for the use 
of Navigators. In this chart all the meridians are repre¬ 
sented by straight lines drawn parallel to each other, and 
the parallels of latitude are also represented by parallel 
straight lines drawn at right-angles to the meridians. 

The chart may be thus constructed. Draw on the lower 
part of the paper a horizontal line to represent the parallel 
of latitude which is to bound the southern portion of the 
chart. From a scale of equal parts, corresponding in size 


















222 


NAVIGATION. 


[BOOK V 


to the extent of the map to be made, lay off, on this line, 
any number of equal distances, and through the pointp 
draw a series of parallels to represent the meridians. 

Then draw a line on the side of the map, and for the 
second parallel of latitude, find from the table of meri 
dional parts the meridional difference of latitude corres 
ponding to the degrees between the first and second par¬ 
allel, and lay off this distance for the interval between the 
two parallels. Then find the meridional difference between 
the second and third, and lay it off in the same way for 
the third parallel, and so on, for the fourth, fifth, &c. 

A place whose latitude and longitude are known, may 
be laid down in the same manner; for it will always be 
determined by the intersection of the meridian and parallel 
of latitude. 

If the chart is constructed on a small scale, the divisions 
on the graduated lines, may be degrees instead of minutes; 
and the meridians and parallels may be drawn only for 
every fifth or tenth degree. 

We have already seen (Art. 23), that the meridional 
difference of latitude bears a constant ratio to the difference 
of longitude, so long as the course remains unchanged: 
and hence we see that on Mercator’s chart, every rhumb 
will be represented by a straight line. 


LINE OF MERIDIONAL -PARTS ON GUNTER’S SCALE. 


25. This scale corresponds exactly with the table of me¬ 
ridional parts, excepting, that in the table, the circle is divid¬ 
ed to minutes, while the scale is divided only to degrees. 
A scale of equal parts is placed directly beneath the scale 
of meridional parts; if the former corresponds to divisions 
of longitude, the latter will represent those of latitude. 
Hence, a chart may be constructed from those scales, by 
using the scale of equal parts for the lines of longitude, 
and the scale of meridional parts for those of latitude. 

w jry 

-/k I 


t L 


fl. i 


/ 

U 


— i 




70 
* o 

* 

i / 

JbJ 


4 






1 0/isuiA. 


11 


Vw 

CcAx\<eJ) 1 j 




4 1/ 


iaA 






A TABLE 


OF 


'LOGARITHMS OF NUMBERS 


FROM 1 TO 10,000. 




L 


_ 


N. 

Log. 

N. 

Log. 

N. 

Log. 

O 

N. 

Log. 

i 

0 • 000000 

26 

1-414973 

5i 

1-707670 

76 

1-880814 

2 

o-3oio3o 

27 

1-431364 

52 

1 *716003 

77 

1-886491 

3 

0-477121 

28 

1-447158 

53 

1-724276 

78 

1-892096 

4 

0-602060 

29 

1-462398 

54 

1-732394 

79 

1-897627 

5 

0-698070 

3o 

1-477121 

55 

1*74o363 

80 

1-908090 

6 

0-778151 

3i 

1-491362 

56 

1-748188 

81 

1-908485 

7 

0-845098 

32 

1-5o5i5o 

57 

1-755875 

82 

1-913814 

8 

0-903090 

33 

1 • 5i8514 

58 

1-763428 

83 

1-919078 

9 

0-904243 

34 

1-531479 

5 9 

1-770852 

84 

1-924279 

IO 

1 • 000000 

35 

I * D44 o 68 

60 

1-778151 

85 

1-929419 

11 

1 -041393 

36 

1-5563o3 

61 

i -785330 

86 

1-934498 

12 

1-079181 

37 

1-568202 

62 

1-792392 

87 

1-939519 

i3 

1•1i 3943 

38 

1-579784 

63 

1-799341 

88 

1-944483 

14 

1•146128 

3 9 

1-591065 

64 

1-806181 

89 

1-949390 

i5 

1•176091 

4o 

1-602060 

65 

1-812913 

90 

1-964243 

16 

I-204120 

4i 

1-612784 

66 

1-819544 

9i 

1-959041 

17 

I•230449 

42 

1-623249 

67 

1-826075 

92 

1-963788 

18 

I-255273 

43 

1-633468 

68 

x-832509 

93 

1-968483 

19 

I-278754 

44 

1 • 643453 

69 

1-838849 

94 

1-973128 

20 

i-3oio3o 

45 | 

1-6532i3 

70 

1-845098 

9 5 

1-977724 

21 

1-322219 

46 

1-662758 

7i 

i-85i258 

96 

1-982271 

22 

I-342423 

47 

1-672098 

72 

1-857333 

97 

1-986772 

23 

I-361728 

48 

1-681241 

73 

1-863323 

98 

1-991226 

24_ 

i-38o2ii 

49 

1-690196 

74 

1-869232 

99 

1-995635 

25 

1-397940 

5o 

1-698970 

75 

1-876061 

100 

2•000000 


Remark. In the following table, in the nine right hand 
columns of each page, where the first or leading figures 
change from 9’s to 0’s, points or dots are introduced in 
stead of the 0’s, to catch the eye, and to indicate that from 
thence the two figures of the Logarithm to be taken from 
the second column, stand in the next line below. 





































2 A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. | 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

IOO 000000 

0434 

0868 

i 3 oi 

1734 

2166 

25 9 8 

3029 

3461 

3891 

432 

IOI 

4321 

4761 

5181 

5609 

6o38 

6466 

6894 

7321 

7748 

8174 

428 

102 

8600 

9026 

945 i 

9876 

®3oo 

®724 

1147 

1570 

i 99 3 

24 i 5 

424 

io3 

012837 

325 9 

368o 

4100 

4521 

4940 

536o 

5779 

6197 

6616 

419 

104 

7o33 

7451 

7868 

8284 

8700 

9116 

9532 

9947 

°36i 

• 77 5 

416 

io5 

021189 

i6o3 

2016 

2428 

2841 

3252 

3664 

4075 

4486 

4896 

412 

106 

53o6 

5-ji5 

6i25 

6533 

6942 

7350 

7 7 5 7 

8164 

8571 

8978 

408 

107 

9 384 

9789 

°i95 

®6oo 

1004 

1408 

1812 

2216 

2619 

3021 

404 

108 

0334^4 

3826 

4227 

4628 

5029 

5430 

583o 

6230 

6629 

7028 

400 

109 

7426 

7825 

8223 

8620 

9017 

9414 

9811 

•207 

. ®6o2 

•998 

3 9 6 

110 

o 4 i 3 9 3 

1787 

2182 

2576 

2969 

3362 

3 7 55 

4148 

4540 

4932 

3 9 3 

111 

5323 

5714 

6io5 

64 9 5 

688o 

7275 

7664 

8o53 

8442 

883o 

38 9 

112 

9218 

9606 

9993 

®38o 

•766 

XI53 

1538 

1924 

2309 

2694 

386 

113 

053078 

3463 

3846 

423o 

4613 

4996 

5378 

5760 

6142 

6524 

382 

114 

6 9 o5 

7286 

7666 

8046 

8426 

88o5 

9i85 

9 563 

9942 

®320 

379 

115 

060698 

1075 

1462 

1829 

2206 

2582 

2 9 58 

3333 

3 7°9 

4o83 

376 

116 

4458 

4832 

52o6 

558o 

5 9 53 

6326 

6699 

7071 

7448 

7815 

372 

117 

8186 

855 7 

8928 

9298 

9668 

°®38 

•407 

®776 

1145 

i 5 i 4 

3 69 

118 

071882 

2250 

2617 

2985 

3352 

3718 

4o85 

4451 

4816 

5182 

366 

n 9 

5547 

5912 

6276 

6640 

7004 

7368 

7 7 3 i 

8094 

8457 

8819 

363 

120 

079181 

9543 

9904 

®266 

•626 

0987 

1347 

1707 

2067 

2426 

36o 

121 

082785 

3144 

35o3 

386i 

4219 

4576 

4984 

5291 

5647 

6004 

357 

122 

63 60 

6716 

7071 

7426 

7781 

8136 

8490 

8845 

9 J 9 8 

9 552 

355 

123 

9905 

®258 

®6i 1 

® 9 63 

1315 

1667 

2018 

2370 

2721 

3071 

35i 

I24_l 

093422 

3772 

4122 

4471 

4820 

6169 

55i8 

5866 

6215 

6562 

349 

125 

6910 

7257 

7604 

79 5 i 

8298 

8644 

8990 

9 335 

9681 

«®26 

346 

126 

100371 

0715 

1059 

i 4 o 3 

1747 

2091 

2434 

2777 

3119 

3462 

343 

127 

3 804 

4146 

4487 

4828 

5 i 6 9 

55io 

5851 

6191 

6531 

6871 

340 

128 

7210 

7549 

7888 

8227 

8565 

8903 

9241 

9 5 79 

9916 

•253 

338 

129 

1io 5 9 o 

0926 

1263 

1599 

1934 

2270 

26o5 

2940 

3275 

8609 

335 

i3o 

1i 3 9 43 

4277 

4611 

4944 

5278 

56i 1 

5 9 43 

6276 

6608 

6940 

333 

131 

7271 

7603 

7934 

8265 

85g5 

8926 

9256 

9 586 

99 l5 

®245 

33o 

132 

120574 

0903 

123 J 

i56o 

1888 

2216 

2544 

2871 

3198 

3525 

328 

133 

3852 

4178 

4604 

483 o 

5156 

5481 

58o6 

6131 

6456 

6781 

325 

i 34 

7io5 

742Q 

7753 

8076 

8399 

8722 

9045 

9368 

9690 

®®i 2 

323 

135 

i 3 o 334 

o655 

0977 

1298 

1619 

1939 

2260 

258o 

2900 

3219 

321 

136 

353 9 

3858 

4177 

4496 

4814 

5133 

5451 

5769 

6086 

64o3 

318 

i 3 7 

6721 

7037 

7354 

7671 

7987 

83o3 

8618 

8 9 34 

9249 

9564 

3x5 

138 

0879 

*194 

®5o8 

*822 

1136 

i 45 o 

1763 

2076 

2389 

2702 

314 

i 3 9 

i 43 oi 5 

3327 

363 9 

3 9 5 i 

4263 

4574 

4885 

5196 

55 o 7 

58i8 

311 

140 

146128 

6438 

6748 

7 o 58 

7367 

7676 

7985 

8294 

86o3 

8911 

309 

141 

9219 

95.27 

9 835 

®I42 

®449 

°-]56 

io63 

1370 

1676 

1982 

307 

142 

152288 

2094 

2900 

32 o 5 

35io 

38i5 

4120 

4424 

4728 

5 o 32 

3o5 

143 

5336 

6640 

5 9 43 

6246 

6549 

6852 

7i54 

7457 

77 5 9 

8061 

3o3 

144 

8362 

8664 

8 9 65 

9266 

9567 

9868 

®i68 

•469 

*769 

1068 

3oi 

145 

161368 

1667 

1967 

2266 

2564 

2863 

3161 

3460 

3 7 58 

4 o 55 

299 

146 

4353 

46 5o 

4947 

5244 

5541 

5838 

6 i 34 

643o 

6726 

7022 

297 

U7 

7317 

7613 

7908 

82 o 3 

8497 

8792 

9086 

9 38 o 

9674 

9968 

295 

148 

170262 

o555 

0848 

1141 

1434 

1726 

2019 

231 X 

26 o 3 

2895 

2 9 3 

149 

3186 

3478 

3769 

4060 

43 51 

4641 

4 9 32 

5222 

55 i 2 

58o2 

291 

i5o 

176091 

638i 

6670 

6959 

7248 

7536 

7825 

8 ii 3 

8401 

8689 

289 

i 5 i 

8 977 

9264 

9 552 

9839 

® 126 

®4 i 3 

®6q 9 

®985 

1272 

1558 

287 

152 

181844 

2129 

24 i 5 

2700 

2 9 85 

3270 

3550 

383 9 

4123 

4407 

285 

153 

4691 

497 5 

525g 

5542 

5825 

6108 

63g 1 

6674 

6966 

7239 

283 

154 

7521 

7803 

8084 

8366 

8647 

8928 

9209 

9490 

9771 

e®5l 

281 

155 

i 9 o 332 

0612 

0892 

1171 

1451 

1730 

2010 

2289 

2667 

2846 

279 

156 

3125 

34 o 3 

368i 

3969 

4237 

4514 

4792 

5069 

5346 

5623 

278 

15 7 

5899 

6176 

6453 

6729 

7005 

7281 

7556 

7832 

8107 

8382 

276 

158 

8667 

8932 

9206 

9481 

9755 

0*29 

®3o3 

•577 

•85o 

1124 

274 

169 

201397 

1670 

1943 

2216 

2488 

2761 

3o33 

33o5 

35 77 

3848 

272 

N. 

0 

1 

2 

3 

1 4 

5 

6 

7 

8 

9 

D. 























































3 


A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

160 

204120 

4391 

4663 

4934 

5204 

5476 

5746 

6016 

6286 

6556 

271 

161 

6826 

7096 

7 365 

7634 

7904 

8173 

8441 

8710 

8979 

9247 

269 

162 

g 5 1 5 

9783 

©» 5 i 

® 3 ig 

•586 

•853 

1121 

1 388 

1 654 

1921 

267 

1 63 

212188 

2454 

2720 

2986 

3252 

35 18 

3783 

4049 

43 1 4 

4679 

266 

164 

4844 

5109 

5373 

5638 

5902 

6166 

6430 

6694 

6957 

7221 

264 

1 65 

7484 

7747 

8010 

8273 

8536 

8798 

9060 

9 323 

g 585 

9846 

262 

166 

220108 

0370 

o 63 i 

0892 

11 53 

1414 

1675 

i 9 36 

2196 

2456 

261 

167 

2716 

2976 

3236 

3496 

3 7 55 

4 oi 5 

4274 

4533 

4792 

5 o 5 i 

259 

168 

53 og 

5568 

5826 

6084 

6342 

6600 

6858 

7115 

7372 

7630 

258 

169 

7887 

8144 

8400 

865 7 

8913 

9170 

9426 

9682 

9938 

•193 

256 

170 

23 o 44 g 

0704 

0960 

12 15 

1470 

1724 

1979 

2234 

2488 

2742 

254 

171 

2996 

325 o 

35 o 4 

3767 

4011 

4264 

4017 

477 ° 

5 o 23 

5276 

253 

172 

5528 

5781 

6 o 33 

6285 

6537 

6789 

7041 

7292 

7544 

7795 

252 

i 7 3 

8046 

8297 

8548 

8799 

9049 

9299 

955 o 

9800 

•• 5 o 

•3 00 

25 o 

174 

240549 

0799 

1048 

1297 

1546 

J 79 5 

2044 

2293 

2541 

2790 

249 

175 

3 o 38 

3286 

3534 

3782 

4 o 3 o 

4277 

4525 

4772 

5019 

5266 

248 

176 

55 1 3 

5759 

6006 

6252 

6'499 

6745 

699 1 

7 23 7 

7482 

7728 

246 

177 

7973 

8219 

8464 

8709 

8954 

9198 

9443 

9687 

9932 

•176 

245 

178 

250420 

0664 

0908 

11 5 i 

1095 

1 638 

1881 

2125 

2368 

2610 

243 

179 

2853 

3096 

3338 

358 o 

3822 

4064 

43 o 6 

4548 

4790 

5 o 3 i 

242 

180 

255273 

55 i 4 

5755 

6996 

6237 

6477 

6718 

6 q 58 

7198 

7439 

241 

181 

7679 

7918 

81 58 

83 9 S 

8637 

8877 

9116 

g 355 

9594 

g 833 

239 

182 

260071 

o 3 io 

0548 

0787 

1025 

1263 

i 5 oi 

1739 

1976 

2214 

238 

1 83 

245 i 

2688 

2925 

3 i 62 

3399 

3636 

3873 

4109 

4346 

4582 

237 

184 

4818 

5 o 54 

5290 

5525 

5761 

6996 

6232 

6467 

6702 

6937 

235 

1 85 

7172 

7406 

7641 

7875 

81 xo 

8344 

85 7 8 

8812 

9046 

9279 

234 

186 

95 i 3 

9746 

9980 

•21 3 

•446 

•679 

•912 

ii 44 

1377 

1609 

233 

187 

271842 

2074 

23 o 6 

2538 

2770 

3 ooi 

3233 

3464 

3696 

3927 

232 

188 

41 58 

4389 

4620 

485 o 

5 o 8 i 

53 11 

5542 

5772 

6002 

6232 

230 

189 

6462 

6692 

6921 

71 5 1 

7380 

7609 

7 838 

8067 

8296 

8525 

229 

190 

278754 

8982 

9211 

943 o 

9667 

9895 

•123 

® 35 i 

•578 

•806 

228 

191 

28 io 33 

1261 

1488 

1715 

1942 

2169 

2396 

2622 

2849 

3075 

227 

192 

33 oi 

3527 

8753 

3979 

42 o 5 

443 1 

4606 

4882 

D107 

5332 

226 

193 

5557 

5782 

6007 

6232 

6456 

6681 

6905 

7i3o 

7354 

7 5 7 8 

225 

194 

7802 

8026 

8249 

8473 

8696 

8920 

9143 

g 366 

g 58 g 

9812 

223 

195 

290035 

0267 

0480 

0702 

0925 

1147 

1 36 g 

1D91 

i 8 i 3 

2 o 34 

222 

196 

2256 

2478 

2699 

2920 

3141 

3363 

3584 

3 804 

4025 

4246 

221 

197 

4466 

4687 

4907 

5 127 

5347 

5567 

5787 

6007 

6226 

6446 

220 

198 

6665 

6884 

7104 

7323 

7642 

7761 

7979 

8198 

8416 

8635 

219 

199 

8853 

9 ° 7 I 

9289 

9507 

9725 

9943 

®i6i 

•378 

•595 

• 3 i 3 

2l8 

200 

3 oio 3 o 

1247 

1464 

1681 

1898 

2114 

233 i 

2547 

2764 

2980 

217 

201 

3 ig 6 

3412 

3628 

3844 

4059 

4275 

4491 

4706 

4921 

5 i 36 

2l6 

202 

535 1 

5566 

5 7 8 i 

5996 

6211 

6425 

6639 

6854 

7068 

7282 

2 l 5 

203 

7496 

7710 

7924 

8137 

835 i 

8564 

8778 

899 1 

9204 

9417 

213 

204 

. 9630 

9843 

®«56 

•268 

•481 

® 6 9 3 

•906 

1118 

i 33 o 

1542 

212 

205 

311754 

1966 

2177 

2389 

2600 

2812 

3 o 23 

3234 

3449 

3656 

21 I 

206 

386 7 

4078 

4289 

4499 

4710 

4920 

5 i 3 o 

5340 

555 i 

5760 

210 

207 

597° 

6180 

6390 

65 99 

6809 

7018 

7227 

7436 

7646 

7854 

209 

208 

8 o 63 

8272 

8481 

8689 

8898 

9106 

9314 

9622 

9730 

9988 

208 

209 

320146 

o 354 

o 562 1 

0769 

0977 

1184 

1391 

1698 

i 8 o 5 

2012 

207 

210 

322219 

2426 

2633 

283 9 

3046 

3252 

3458 

3665 

3871 

4077 

206 

2 11 

4282 

4488 

4694 

4899 

5 io 5 

53 10 

55 16 

5721 

5926 

61 3 1 

205 

212 

6336 

654 i 

6745 

6950 

7105 

7359 

7563 

7767 

7972 

8176 

204 

2 l 3 

838 o 

8583 

8787 

8991 

9 1 94 

9 3 9 8 

9601 

9806 

«s»®g 

•211 

203 

214 

33 o 4 i 4 

0617 

0819 

1022 

1225 

1427 

i 63 o 

1 832 

2 o 34 

2236 

202 

2 l 5 

2438 

2640 

2842 

3 044 

3246 

3447 

364 g 

385 o 

4 o 5 i 

4253 

202 

2l6 

4454 

4655 

4856 

5o5~i 

5257 

5458 

5658 

5809 

6 o 5 g 

6260 

201 

217 

6460 

6660 

6860 

7060 

7260 

7459 

7 65 g 

7868 

8 o 58 

8257 

200 

210 

8456 

8656 

8855 

9054 

9253 

945 1 

9600 

9849 

0047 

•246 

’99 

219 

340444 

0642 

0841 

1039 

1237 

1435 

1 63 2 

i 83 o 

2028 

2225 

198 

. N. 

0 

1 1 

2 


4 1 

1 

5 

_L 

6 

V 

8 

9 

D. 


15 





























































i A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


1 N - 

0 

1 

1 1 

2 

3 

4 

5 

6 

7 

8 

! 

1 9 

D. 

220 

342423 

2620 

2817 

3 oi 4 

3212 

3409 

36 o 6 

38 o 2 

3999 

1 , 

4196 

>97 

221 

4392 

4589 

4785 

4981 

5 l 78 

5374 

5570 

5766 

5962 

6137 

196 

222 

6353 

6649 

6744 

6939 

7 l 35 

733 o 

7020 

7720 

7910 

8110 

195 

223 

83 o 5 

85 oo 

8694 

8889 

9 083 

9278 

9472 

9666 

9860 

©054 

194 

224 

300248 

0442 

o 636 

0829 

1023 

1216 

1410 

i 6 o 3 

1796 

1989 

193 

220 

21 83 

2376 

2568 

2761 

2954 

3 147 

333 9 

3532 

3724 

3916 

193 

226 

4108 

43oi 

449 ^ 

4685 

4876 

5 o 68 

5260 

5452 

5643 

5834 

192 

227 

6026 

6217 

6408 

6399 

6790 

6981 

1 7172 

7363 

7334 

7744 

1 9 1 

228 

7 9 35 

8 i 25 

83 16 

85 o 6 

8696 

8886 

9076 

9266 

9456 

9646 

190 

229 

9880 

«®25 

® 21 5 

® 4 o 4 

® 5 9 3 

•783 

•972 

1161 

i 35 o 

i539 

189 

23o 

361728 

1917 

2105 

2294 

2482 

2671 

2869 

3 o 48 

3236 

3424 

188 

23 I 

36 12 

3 800 

3988 

4178 

4363 

4301 

4739 

4926 

5 11 3 

53 oi 

188 

232 

5483 

56 7 5 

5362 

6049 

6236 

6423 

6610 

6796 

6983 

7169 

187 

233 

7356 

7542 

7729 

7 9 i5 

8101 

8287 

8473 

8609 

8845 

qo3o 

186 

234 

9216 

9401 

9 58 7 

9772 

9958 

®U 3 

•328 

• 5 i 3 

•698 

•883 

1 85 

235 

371068 

1253 

1437 

1622 

1806 

1 99 1 

2175 

236 o 

2644 

2728 

184 

236 

291 2 

3096 

3280 

3464 

3647 

383 1 

4 oi 5 

4198 

4382 

4565 

184 

237 

4748 

4982 

5 i i 5 

5298 

5481 

5664 

5846 

6029 

6212 

6894 

1 S 3 

238 

6677 

6709 

6942 

7124 

7306 

7488 

7670 

7862 

8084 

8216 

182 

239 

83 9 8 

858 o 

8761 

8943 

9124 

93 o 6 

9487 

9668 

9849 

®* 3 o 

181 

240 

380211 

0392 

o 5 ~ j 3 

0764 

0934 

111 5 

1296 

1476 

1 656 

1837 

181 

241 

2017 

2197 

2377 

2557 

2737 

2917 

3 o 97 

3277 

3456 

3636 

180 

242 

38 1 5 

8996 

4174 

4353 

4533 

4712 

4891 

5070 

5249 

5428 

>79 

243 

56 o 6 

5735 

6964 

6142 

6321 

6409 

6677 

6856 

7034 

7212 

178 

244 

7390 

7568 

7746 

7923 

8101 

8279 

8436 

8634 

8811 

8989 

178 

245 

9166 

9343 

9620 

9698 

9875 

®® 5 i 

•228 

®4o5 

•582 

•709 

>77 

246 

3qoq35 

1112 

1288 

1464 

1641 

1817 

i 99 3 

2169 

2345 

2521 

176 

247 

2697 

2873 

3048 

3224 

34 oo 

3575 

3761 

3926 

4101 

4277 

>76 

248 

4452 

4627 

4802 

4977 

5 1 52 

5326 

0301 

5676 

585 o 

602 5 

175 

249 

6199 

6874 

6548 

6722 

6896 

7071 

7245 

7419 

7392 

7766 

>74 

25o 

397940 

8114 

8287 

8461 

8634 

8808 

8981 

9154 

9328 

95oj 

173 

25i 

9674 

9847 

0*20 

0192 

•365 

•538 

•711 

•883 

io 56 

1228 

173 

252 

401401 

1673 

1745 

1917 

2089 

2261 

2433 

26o5 

2777 

2949 

172 

253 

3 121 

3292 

3464 

3635 

3807 

3 97 8 

4149 

4320 

4492 

4663 

> 7 

254 

4834 

5 oo 5 

5176 

5346 

55 i 7 

5688 

5858 

6029 

6199 

6370 

> 7 > 

255 

6540 

6710 

6881 

7o5i 

7221 

7391 

756i 

7731 

7901 

8070 

170 

256 

8240 

8410 

8079 

8749 

8918 

9087 

9237 

9426 

95 g 5 

9764 

169 

257 

9933 

® 102 

•27c 

® 44 o 

•609 

a 777 

•946 

1114 

1283 

145 1 

169 

258 

4i1620 

1788 

1956 

2124 

2293 

2461 

2629 

2796 

2964 

3 1 32 

168 

259 

33 oo 

3467 

3635 

38 o 3 

3970 

4 i 37 

43o5 

4472 

4639 

4806 

167 

260 

4 U 973 

5i4o 

5307 

5474 

5641 

5 808 

3974 

6141 

63 o 8 

6474 

167 

261 

6641 

6807 

6973 

7 i3 9 

73 o 6 

7472 

7633 

7804 

7970 

81 35 

166 

262 

83 oi 

8467 

8633 

8798 

8964 

9129 

9295 

9460 

9625 

979 1 

1 65 

263 

9956 

® 121 

•286 

® 45 i 

•616 

•781 

®945 

1110 

1275 

1489 

1 65 

264 

421604 

1788 

io 33 

2007 

2261 

2426 

2690 

2754 

2918 

3o82 

164 

265 

3246 

3410 

3074 

3747 

3901 

4 o 65 

4228 

4392 

4555 

4718 

164 

266 

4882 

5 o 45 

5208 

5371 

5534 

6697 

0860 

6023 

6186 

6349 

1 63 

267 

65 11 

6674 

6836 

6999 

7161 

7324 

7486 

7848 

7811 

7973 

162 

268 

81 35 

8297 

8469 

8621 

8783 

8944 

9106 

9268 

9429 

9391 

162 

269 

97 52 

99 1 4 

•075 

•236 

•398 

•559 

•720 

®88i 

1042 

1203 

161 

270 

43 I 354 

1 525 

1 685 

1846 

2007 

2167 

2328 

2488 

2649 

2809 

161 

271 

2969 

3 i 3 o 

3290 

345 o 

36 io 

3770 

3 g 3 o 

4090 

4249 

4409 

160 

272 

4569 

4729 

4888 

5 o 48 

5207 

5367 

5526 

5685 

5844 

6004 

169 

273 

61 63 

6322 

6481 

6640 

6708 

6957 

7116 

7275 

7433 

7392 

i5q 

274 

773 i 

7909 

8067 

8226 

8384 

8542 

8701 

885 9 

9017 

9175 

i58 

275 

9333 

9491 

9648 

9806 

9964 

® 122 

•279 

° 43 7 

•394 

•752 

1 58 

276 

440909 

1066 

1224 

i 38 i 

1 538 

1696 

1 852 

2009 

2166 

2323 

157 

2 77 

2480 

2637 

2793 

2 o5o 

3 106 

3263 

3419 

3576 

3732 

3889 

>37 

278 

4 o 45 

4201 

4337 

45i3 

4669 

4825 

4981 

5 137 

5293 

5449 

i 36 

279 

56o4 

5760 

59 i 5 

6071 

6226 

6382 

6537 

6692 

6848 

7003 

1 55 

N. 

0 

I 

2 

3 

4 

5 

6 

7 

8 

9 

D. 








































































A TABLE OF LOGARITHMS FROM 1 TO 10,000. 5 


N. 

0 

I 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

280 

447158 

73 3 

7468 

7623 

7778 

7933 

8088 

8242 

8397 

8552 

155 

281 

I 8706 

8861 

9010 

9170 

9324 

9478 

9633 

9787 

9941 

e® 9 5 

154 

282 

470249 

o 4 o 3 

0007 

0711 

o865 

1018 

1172 

1326 

U79 

1633 

154 

283 

1786 

1940 

2093 

2247 

2400 

2553 

2706 

2869 

3oi 2 

3165 

153 

284 

3318 

347 1 

3624 

3 777 

3g3o 

4082 

4235 

4387 

4540 

4692 

153 

285 

4845 

4997 

515o 

53 o 2 

0454 

56o6 

3738 

6910 

6062 

6214 

132 

286 

6366 

6518 

6670 

6821 

6973 

7125 

7276 

7428 

7779 

7731 

132 

287 

7882 

| 8o33 

8184 

833o 

8487 

8638 

8789 

8940 

9091 

9242 

151 

288 

9392 

| 9 5 43 

9694 

9845 

9995 

*146 

*296 

®447 

®397 

•748 

151 

289 

460898 

1048 

1198 

1348 

1 499 

1649 

<799 

1948 

2098 

2248 

i5o 

29a 

462398 

2548 

2697 

2847 

2 997 

3 i 46 

3296 

3445 

3594 

3744 

i5o 

291 

3 89 3 

4042 


4340 

4490 

4639 

4708 

4936 

5o8o 

5234 

149 

292 

5383 

5532 

56oo 

5829 

^977 

6126 

6274 

6423 

6571 

6719 

149 

293 

6868 

7016 

7164 

7312 

746o 

7608 

7736 

7904 

8o52 

8200 

148 

294 

8347 

8496 

8643 

8790 

8 9 38 

9085 

9233 

9380 

9527 

9675 

148 

293 

9822 

9969 

®! l6 

°263 

®410 

° 55 ~i 

•704 

•851 

*998 

1145 

147 

296 

471292 

1438 

1585 

1732 

1878 

2025 

2171 

2318 

2464 

26iO 

146 

2 97 

2766 

2903 

3049 

3l 0 

3341 

3487 

3633 

3779 

3925 

4071 

146 

298 

4216 

4362 

45 o 8 

4633 

4799 

4944 

6090 

5233 

5381 

5526 

146 

299 

5671 

5816 

5962 

6107 

6252 

6397 

6542 

6687 

6832 

6976 

145 

3oo 

477121 

7266 

74 u 

7555 

7700 

7844 

7989 

8133 

8278 

8422 

U5» 

3oi 

8566 

8711 

8855 

8999 

9143 

9287 

9431 

9 5 7 5 

9719 

9863 

144 

302 

480007 

oi 5 i 

0294 

0438 

o 582 

0726 

0869 

1012 

1156 

1299 

144 

3o3 

1443 

1586 

1 7129 

1872 

2016 

2129 

2302 

2445 

2588 

2~l'3l 

143 

3 04 

2874 

3oi6 

3109 

33 o 2 

3445 

3587 

3730 

3872 

4015 

4157 

M3 

3o5 

43 oo 

4442 

4585 

4727 

4860 

5oi ! 

5153 

5295 

5437 

5579 

142 

3o6 

5721 

5863 

6oo5 

6147 

6289 

643 g 

6372 

6714 

6855 

6997 

142 

3o7 

7138 

7280 

742! 

7563 

7704 

7845 

7986 

8127 

8269 

8410 

141 

3o8 

855 j 

8692 

8833 

8974 

9> '4 

9255 

9 3 9 6 

9537 

9 6 77 

9818 

141 

309 

9908 

®*99 

®239 

•38o 

®520 

®66i 

®8oi 

®94i 

1081 

1222 

140 

310 

491862 

i 5 o 2 

1642 

1782 

1922 

2062 

220! 

234 i 

2481 

2621 

140 

3i 1 

2760 

2900 

3 040 

3179 

3319 

3458 

3597 

3737 

3876 

4015 

139 

312 

4 i 55 

4294 

4433 

4672 

4711 

485 o 

4989 

5i28 

5267 

5406 

139 

313 

5544 

5683 

5822 

5960 

6099 

6238 

63 76 

6515 

6653 

6791 

139 

314 

6930 

7068 

7206 

7 3 44 

7483 

7621 

77 5 9 

7897 

8o35 

8173 

r38 

315 

83 n 

8448 

8386 

8724 

8S62 

8999 

Oi37 

9275 

04l2 

9550 

138 

316 

_ 9687 

9824 

9962 

®*99 

®236 

* 3 74 

®5l I 

•648 

®785 

*922 

ii7 

317 

5o1 o 5 q 

1196 

1333 

1470 

1607 

1744 

|88o 

2017 

2154 

229I 

i 3 7 

318 

2427 

2564 

2700 

2837 

2973 

3109 

3246 

3382 

3518 

3633 

136 

319 

3791 

3927 

4o63 

4199 

^335 

447* 

4607 

4743 

4878 

5oi4 

136 

320 

5o5f5o 

5286 

5421 

5557 

56 9 3 

5828 

5964 

6099 

6234 

6370 

136 

321 

65o5 

6640 

6776 

6911 

7046 

71 H 1 

7016 

7401 

7 586 

7721 

135 

322 

7856 

799 1 

8126 

8260 

83 9 5 

853o 

8664 

8799 

8934 

9068 

135 

323 

9203 

9337 

9471 

9606 

9740 

9874 

©eog 

®i43 

•277 

®4i 1 

i 34 

324 

5 io 545 

0679 

0813 

0917 

1081 

1215 

1349 

1482 

1616 

i ~] 5 o 

134 

325 

1883 

2017 

2151 

2284 

2418 

2351 

2684 

2S18 

2951 

3 084 

i33 

326 

3218 

3351 

3484 

3617 

375o 

3883 

40l6 

4149 

4282 

44i 4 

133 

327 

4548 

4681 

48 i 3 

4946 

5079 

52! I 

5344 

5476 

5609 

5741 

j 33 

328 

5874 

6006 

6139 

6271 

64o3 

6535 

6668 

6800 

6932 

7064 

132 

329 

7196 

7828 

7460 

7 5 9 2 

7724 

7855 

7987 

8119 

8251 

8382 

132 

33 0 

5i85i4 

8646 

S777 

8909 

9040 

9171 

9 3 o3 

9434 

g 566 

9697 

j 31 

33 

9828 

9969 

®°90 

®22 I 

•353 

*484 

*6 i 5 

C745 

•876 

1007 ! 

131 

332 

321138 

1269 

1400 

i53o 

1661 

1792 

1922 

2053 

2183 

2314 i 

131 

333 

2444 

2570 

2705 

2835 

2966 

8096 

3226 

3356 

3486 

3616 

i3o 

334 

3746 

3876 

4006 

4136 

4266 

4896 

4526 

4656 

4785 

49i5 

i3o 

335 

5 o 45 

5174 

53 o 4 

5434 

5563 

56g3 

5822 

5951 

6081 

6210 

129 

336 

633 9 

6469 

6698 

6727 

6856 

6980 

7114 

7243 

7372 

7601 

129 

337 

7630 

77 5 9 

7888 

8016 

8146 

8274 

8402 

8531 

8660 

8788 

129 

338 

8 9 >7 

9046 

9H4 

9302 

943o 

9639 

9687 i 

9 8 i 5 

9943 


128 

339 

d 30200| 

o 328 

I 

0456 | 

o584 

0712 

0840 I 

0968 | 

1096 

1223 

i35i 

128 

N. 

0 1 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 





































































































6 A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. 

( 

0 

1 1 

1 

! 2 

3 

4 

5 

6 

! 7 

j 8 

9 

j D. 

340 

531479 

1607 

1734 

1862 

1990 

2117 

2245 

2372 

1 2500 

2627 

128 

341 

2754; 2882 

3009 

3 i 36 

3264 

3391 

35 i 8 

3645 

3772 

3899 

127 

342 

4026 

41 53 

4280 

4407 

4534 

4661 

4787 

4 qi 4 

5 o 4 i 

5 i 67 

127 

343 

5294 

5421 

5547 

56 7 4 

58 oo 

5927 

6 o 53 

j 6180 

63 o 6 

6432 

126 

344 

6558 

6685 

6811 

6 9 3 7 

7063 

7189 

7 3 1 5 

! 744 i 

7567 

7693 

126 

345 

7819 

! 7945 

8071 

8197 

8322 

8448 

85 7 4 

8699 

8825 

8 9 5 1 

126 

346 

9076 

9202 

9327 

9452 

9 5 7 8 

97°3 

9829 

99 5 4 

**79 

•204 

125 

347 

540329 

0455 

o 58 o 

o 7 o 5 

o 83 o 

0935 

1080 

1205 

i 33 o 

1454 

125 

34a 

1579 

j n °4 

1829 

1953 

2078 

2203 

2327 

2452 

25 7 6 

2701 

1 25 

349 

2825 

! 2960 

3o 7 4 

3 i 99 

3323 

3447 

35 7 1 

3696 

3820 

3 944 

124 

35 o 

544068 

4192 

43 i 6 

4440 

4564 

4688 

4812 

4936 

5 o 6 o 

5 1 83 

124 

351 

53 o 7 

543 i 

5555 

56 7 8 

58 o 2 

5925 

6049 

6x72 

6296 

6419 

124 

352 

6543 

6666 

6789 

6913 

7 o 36 

7 i 5 9 

7282 

74o5 

7629 

7 652 

123 

353 

7775 

7898 

8021 

8 i 44 

8267 

83 89 

85 i 2 

8635 

8 7 58 

8881 

123 

354 

9003 

9126 

9249 

9 3 7 i 

9494 

9616 

9739 

9861 

9984 

®xo6 

123 

355 

550228 

o 35 i 

0473 

0595 

0717 

0840 

0962 

1084 

1206 

1328 

122 

356 

i 45 o 

l 5 7 2 

1694 

1816 

1938 

2060 

2181 

23 o 3 

2425 

2547 

122 

357 

2668 

2790 

2911 

3 o 33 

3 1 55 

3276 

33 9 8 

35 i 9 

364 o 

3762 

I 2 X 

35 b 

3883 

4004 

4126 

4247 

4368 

4489 

4610 

4 7 3 1 

4852 

4973 

121 

359 

0094 

5215 

5336 

5457 

55 7 8 

5699 

5820 

5940 

6061 

6x82 

I 21 

*360 

5563 o 3 

6423 

6544 

6664 

6 7 85 

6 go 5 

7026 

7146 

7267 

7387 

120 

36 i 

7 5 o 7 

7627 

7748 

7868 

7988 

8108 

8228 

8349 

8469 

858 9 

120 

362 

8709 

8829 

8948 

9068 

9188 

9808 

9428 

9548 

0667 

9787 

120 

363 

99°7 

*•26 

®i 46 

•265 

•385 

• 5 o 4 

•624 

*743 

•863 

•982 

Iig 

364 

56 i101 

1221 

1 34 o 

1469 

1 5 7 8 

1698 

1817 

ig 36 

2o55 

2174 

II 9 

365 

2293 

2412 

253 i 

265 o 

2769 

2887 

3 oo 6 

3 i 25 

3244 

3362 

ug 

366 

3481 

36 oo 

3 7 i 8 

383 7 

3955 

4074 

4192 

43 11 

4429 

4548 

Iig 

367 

4666 

4784 

4903 

5 o 2 I 

5 139 

525 7 

53 7 6 

5494 

5612 

5 7 3 o 

118 

36 b 

5848 

6966 

6084 

6202 

6320 

6437 

6555 

66 7 3 

6791 

6909 

Il8 

369 

7026 

7 U 4 

7262 

7379 

7497 

7614 

7732 

7849 

7967 

8084 

Il8 

370 

568202 

83 19 

8436 

8554 

8671 

8788 

8905 

9023 

9140 

9257 

117 

371 

9 3 74 

9491 

9608 

9725 

9842 

9959 

c® 7 6 

®i 9 3 

® 3 o 9 

•426 

117 

3 7 2 

5 7 o 543 

0660 

0776 

0893 

1010 

1126 

1243 

i 35 g 

1476 

i 5 g 2 

117 

3 7 3 

1709 

1825 

1942 

2 o 58 

2174 

2291 

2407 

2523 

2639 

2765 

Il6 

3 7 .4 

2872 

2988 

3 io 4 

3220 

3336 

3452 

3568 

3684 

3800 

3 gx 5 

Il6 

3 7 5 

4 o 3 i 

4 i 47 

4263 

4379 

4494 

4610 

4726 

4841 

4967 

6072 

116 

3 7 6 

5 188 

53 o 3 

5419 

5534 

565 o 

5 7 65 

588 o 

5 gg 6 

6111 

6226 

1 1 5 

377 

634 i 

6457 

65 7 2 

6687 

6802 

6917 

7032 

7147 

7262 

7377 

11 5 

37b 

7492 

7607 

7722 

7 836 

79 5 i 

8066 

8181 

8295 

84 io 

8525 

ii 5 

379 

0639 

8754 

8868 

8 9 83 

9°97 

9212 

9326 

9441 

9 555 

9669 

H 4 

38 o 

579784 

9898 

®®i 2 

•126 

•241 

• 35*5 

•469 

®583 

•697 

®8n 

114 

38 i 

58 og 25 

1039 

11 53 

1267 

i 38 i 

i 4 q 5 

1608 

1722 

1 836 

ig 5 o 

H 4 

382 

2063 

2177 

2291 

2404 

25 i 8 

26J1 

2745 

2858 

2972 

3 o 85 

114 

383 

3199 

33 12 

3426 

3539 

3652 

3 7 65 

38 7 9 

8992 

4io5 

4218 

1 13 

384 

433 1 

4444 

4557 

4670 

4783 

4896 

5009 

5 x 22 

5235 

5348 

ii 3 

385 

5461 

55 7 4 

5686 

5 79 o 

5912 

6024 

6 i 3 7 

6250 

6362 

6475 

ii 3 

386 

658 7 

6700 

6812 

6925 

7037 

7149 

7262 

7374 

7486 

7699 

112 

887 

77 11 

7823 

79 35 

8047 

8160 

8272 

8384 

8496 

8608 

8720 

112 

388 

8832 

8944 

9 o 56 

9167 

9279 

9391 

95 o 3 

96 x 5 

9726 

9838 

112 

389 

9950 

•®6i 

®i 7 3 

•284 

•396 

® 5 o 7 

*619 

® 73 o 

•842 

• 9 53 

112 

390 

591065 

1176 

1287 

1 3 99 

i 5 io 

1621 

I 7 32 

1843 

i 9 55 

2066 

111 

391 

2177 

2288 

2399 

25 io 

2621 

2 7 32 

2843 

2954 

3064 

3 x 7 5 

in 

392 

3286 

3397 

35 o 8 

36 i 8 

37 2 9 

3840 

3 g 5 o 

4061 

4171 

4282 

111 

898 

4393 

45 o 3 

4614 

4724 

4834 

4945 

5 o 55 

5 i 65 

5276 

5386 

110 

394 

6496 

56 o 6 

5717 

5827 

5 9 37 

6047 

61 5 7 

6267 

6377 

6487 

110 

395 

6397 

6707 

6817 

6927 

7037 

7146 

7256 

7366 

7476 

7 586 

110 

396 

7695 

7 8 o 5 

79*4 

8024 

8 i 34 

8243 

8353 

8462 

85 7 2 

868x 

IIO 

397 

8791 

8900 

9009 

9 H *9 

9228 

9337 

9446 

9556 

9665 

9774 

109 

398 

9883 

999 2 

*IOI 

®210 

•819 

•428 

® 53 7 

•646 

• 7 55 

•864 

109 

399 

600973 

1082 

1191 

I2 99 

1408 

i 5 i 7 

1626 

1734 

1843 

i 9 5 i 

109 

N. 

1 _ 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 








































































7 


A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

4oo 

602060 

2169 

2277 

2386 

2494 

2603 

2711 

2819 

2928 

3o36 

108 

401 

3144 

3253 

336i 

3469 

3577 

3686 

3794 

3902 

4010 

4118 

108 

402 

4226 

4334 

4442 

455 o 

4658 

4766 

4874 

4982 

5o8 9 

5197 

108 

4 o 3 

53o5 

5413 

5521 

5628 

5 7 36 

5844 

5961 

bo 5 g 

6166 

6274 

108 

404 

638i 

6489 

6596 

6704 

6811 

6919 

7026 

7i33 

'7241 

7348 

107 

4 o 5 

7455 

7562 

7669 

7777 

7884 

7991 

8098 

8205 

83i2 

8419 

I0 7 

406 

8526 

8633 

8740 

8847 

8954 

9061 

9167 

9274 

9381 

9488 

107 

407 

9594 

9701 

9808 

9914 

°®21 

•128 

•234 

•34l 

•447 

•554 

107 

408 

610660 

0767 

0873 

°979 

I086 

1192 

1298 

i 4 o 5 

i 5 ii 

1617 

106 

409 

1723 

1829 

1936 

2042 

2148 

2234 

236 o 

2466 

2572 

2678 

106 

410 

612784 

2890 

2996 

3l02 

3207 

3313 

34x9 

3525 

363o 

3736 

106 

411 

3842 

3947 

4o53 

4169 

4264 

4370 

4475 

4581 

4686 

4792 

106 

412 

4897 

5oo3 

5 io 8 

6213 

5319 

5424 

5529 

5634 

5740 

5845 

io5 

4 i 3 

5900 

6o55 

6160 

6265 

6370 

6476 

6581 

6686 

6790 

68 9 5 

io5 

4i4 

7000 

7io5 

7210 

7315 

7420 

7525 

7629 

7734 

7 83 9 

7943 

io5 

4 i 5 

8048 

8153 

8257 

8362 

8466 

8571 

8676 

8780 

8884 

8989 

io5 

4 i 6 

9093 

9 J 9 8 

9302 

9406 

95 ii 

9615 

9719 

9824 

9928 

**32 

104 

417 

62oi36 

0240 

o344 

0448 

o 552 

o656 

0760 

0864 

0968 

1072 

104 

418 

1176 

1280 

1384 

1488 

1092 

1695 

1799 

1903 

2007 

2110 

104 

419 

2214 

23 i 8 

2421 

2525 

2628 

2782 

2835 

2 9 3 9 

3042 

3 i 46 

104 

420 

623249 

3353 

3456 

3559 

3663 

3766 

3869 

3973 

4076 

4179 

io3. 

421 

4282 

4385 

4488 

4591 

4696 

4798 

4901 

5004 

5107 

52X0 

io3 

422 

5312 

54 i 5 

55i8 

5621 

6724 

5827 

5929 

6o32 

6135 

6238 

io3 

423 

634o 

6443 

6546 

6648 

6761 

6853 

6956 

7 o 58 

7161 

7263 

io3 

424 

7366 

7468 

7671 

7673 

777 5 

7878 

7980 

8082 

8i85 

8287 

102 

425 

83 89 

8491 

85 9 3 

8695 

8797 

8900 

9002 

9104 

9206 

9308 

102 

426 

9410 

9512 

9613 

97 1 5 

9817 

99*9 

*•21 

•123 

•224 

*326 

102 

427 

630428 

o53o 

o63i 

0733 

o835 

0936 

io38 

1139 

1241 

1342 

102 

428 

1444 

i 545 

1647 

1748 

1849 

1961 

2052 

2153 

2255 

2356 

IOI 

429 

2457 

2559 

2660 

2761 

2862 

2963 

3o64 

3x65 

3266 

336 7 

IOI 

43 0 

633468 

3569 

3670 

3771 

3872 

3 97 3 

4074 

4175 

4276 

4376 

100 

431 

4477 

4578 

467Q 

4779 

4880 

4981 

5o8i 

5182 

5283 

5383 

100 

432 

5484 

5584 

5685 

5 7 85 

5886 

5o86 

6087 

6187 

6287 

6388 

100 

433 

6488 

6588 

6688 

6789 

6889 

6989 

7089 

7189 

7290 

7890 

100 

434 

7490 

7590 

7690 

7790 

7890 

7990 

8090 

8190 

8200 

8889 

99 

435 

8489 

8689 

8689 

8789 

8888 

8988 

9088 

9'g 3 

9287 

9887 

99 

436 

9486 

9 586 

9686 

9780 

9880 

9984 

**84 

® 183 

*283 

*382 

99 

437 

640481 

o58i 

0680 

°779 

0879 

0978 

1077 

1177 

1276 

i3-]5 

99 

438 

U74 

1573 

1672 

1771 

1871 

1970 

2069 

2168 

2267 

2366 

99 

439 

2465 

2563 

2662 

2761 

2860 

2959 

3o58 

3156 

3255 

3354 

99 

440 

643453 

355i 

365o 

3749 

3847 

3946 

4044 

4143 

4242 

4340 

98 

44i 

4439 

4537 

4636 

4734 

4832 

493i 

5029 

5127 

5226 

5324 

98 

442 

5422 

5521 

5619 

5717 

58i5 

5913 

6011 

6110 

6208 

63o6 

98 

443 

6404 

65 o 2 

6600 

6698 

6796 

6894 

6992 

7089 

7187 

7285 

9§ 

444 

7383 

748 i 

7579 

7676 

7774 

7872 

7969 

8067 

8165 

8262 

98 

445 

836o 

8458 

8555 

8653 

8760 

8848 

8945 

9043 

9140 

9 2 87 

97 

446 

9 335 

9432 

953o 

9627 

9724 

9821 

99*9 

«®i6 

®ii 3 

•210 

97 

447 

65o3o8 

040 5 

0502 

0599 

0696 

o 79 3 

0890 

0987 

1084 

1181 

97 

44» 

1278 

1375 

U72 

1569 

1666 

1762 

1869 

1966 

2 o 53 

2l5o 

97 

449 

2246 

2343 

2440 

2536 

2633 

2730 

2826 

2923 

3019 

3116 

97 

45o 

6532i3 

33o9 

34o5 

35o2 

3598 

36 9 5 

3791 

3888 

3984 

4080 

9^ 

451 

4177 

4273 

4369 

4465 

4562 

4658 

4754 

485o 

4946 

5 o 42 

96 

452 

5138 

5235 

5331 

5427 

5523 

56ig 

5~ii5 

58io 

6906 

6002 

96 

453 

6098 

6194 

6290 

6386 

6482 

6577 

66 7 3 

6769 

6864 

6960 

96 

454 

7006 

7102 

7 2 47 

7343 

7438 

7534 

7629 

7725 

7820 

7916 

96 

455 

8011 

8107 

8202 

8298 

83 9 3 

8488 

8584 

8679 

8774 

8870 

9^ 

456 

8 9 65 

9060 

9i55 

9260 

9346 

9441 

9 536 

9631 

9726 

9821 

9 5 

457 

9916 

••n 

•106 

® 201 

•296 

•391 

*486 

•58i 

•676 

•771 

95 

458 

66o&65 

0960 

io55 

1 i5o 

1245 

i 339 

1434 

1629 

1623 

1718 


459 

i8i3 

1907 

2002 

2096 

2191 

2286 

238o 

2476 

2569 

2663 

9 5 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 










































8 A TABLE OF LOGARITHMS FROM 1 TO 10 , 000 . 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

1 

8 

9 

D. 

460 

662753 

2S52 

2947 

3 o 4 i 

3135 

323 o 

3324 

34i8 

3512 

3607 

94 

461 

3701 

3795 

3889 

3988 

4078 

4172 

4266 

436o 

4404 

4543 

94 

462 

4642 

4786 

483 0 

4924 

5oi8 

5i 12 

5206 

0299 

5398 

5487 

94 

403 

5581 

567 5 

5769 

5862 

0906 

6000 

6143 

6287 

6331 

6424 

94 

464 

6518 

6612 

6700 

6/ 99 

6892 

6986 

7079 

7 1 73 

7266 

780 0 

94 

465 

7453’ 

7646 

7640 

7/83 

7826 

792° 

8013 

8106 

8199 

8298 


466 

8386 

8479 

8072 

8660 

8709 

8802 

8940 

9 o 38 

9131 

9224 

9 3 

467 

o3i7 94io 

9608 

9096 

9689 

9782 

9870 

9967 

°®6o 

53 

9 3 

408 

670246’ 

0J39 

0481 

0024 

0617 

0710 

0802 

0890 

0988 

1000 


469 

1173 

1260 

1353 

1401 

1543 

1636 

1728 

1821 

1913 

2005 

9 3 

470 

672098 

2190 

2283 

2375 

2467 

256 o 

2652 

2744 

2336 

2929 

92 

471 ' 

302 1 

3113 

3200 

3297 

3890 

3482 

3574 

3666 

3768 

38oo 

92 

472 

3942 

4 o 34 

4126 

4218 

4810 

4402 

4494 

4586 

4677 

4769 

92 

473 

4861 

4933 

0043 

6187 

0228 

5320 

5412 

55o3 

5og5 

5687 

92 

474 

5778 

5870 

5962 

6o53 

6140 

6286 

6328 

6419 

6011 

6602 

92 

475 

6694 

6786 

6076 

6968 

7009 

7151 

7242 

7333 

7424 

7016 

9 1 

476 

7607 

7698 

77^9 

7881 

7972 

8o63 

8104 

8245 

8336 

8427 

9* 

477 

8518 

8609 

8700 

8791 

8882 

8973 

9064 

9100 

9246 

9 33 7 

9 1 

474 

9423 

9 5 1 9 

9610 

9700 

979' 

9882 

9978 

® a 63 

® 154 

®243 

9 1 

479 

68o336 

0426 

o517 

0607 

0698 

0789 

0879 

0970 

1060 

1151 

9i 

43 o 

681241 

1332 

1422 

1513 

i6o3 

1693 

1784 

1874 

1964 

2000 

90 

43 i 

2 145 

22 35 

2826 

2416 

2606 

2590 

2686 

2777 

2867 

2907 

90 

482 

3 o 47 

3137 

3227 

3317 

3407 

3497 

3587 

36 7 7 

3767 

3857 

90 

483 

3947 

4037 

4127 

4217 

4307 

4396 

4486 

4876 

4666 

4706 

90 

484 

4^45 

4935 

5020 

0114 

5204 

6294 

5383 

5478 

5563 

5652 

90 

485 

5 7 42 

5 831 

5921 

6010 

6100 

6189 

6279 

6363 

6458 

6547 

89 

486 

6636 

6726 

6815 

6904 

6994 

7088 

7172 

7261 

735 i 

7440 

o 9 

487 

7629 

7618 

77°7 

779' J ' 

7806 

797? 

8064 

8153 

8242 

8331 

Q 9 

488 

8420 

8509 

8098 

6667 

8776 

8860 

8908 

9042 

9131 

9220 

o 9 

489 

9309 

9398 

9486 

9670 

9664 

9753 

9841 

9930 

@3,9 

•107 

89 

49° 

690196 

0285 

0373 

0462 

o55o 

o 63 q 

0728 

0816 

0905 

0993 

89 

491 

1081 

1170 

1208 

1847 

1435 

1024 

1612 

1700 

1789 

1877 

83 

492 

1965 

2003 

2142 

2280 

23 18 

2406 

2494 

2 583 

2671 

2709 

88 

493 

2847 

2935 

3 o 23 

3111 

3 i 99 

3287 

3370 

3463 

3551 

363 9 

83 

494 

3727 

3815 

3903 

8991 

4078 

4166 

4204 

4342 

443o 

45i7 

88 

495 

46o5 

4693 

4781 

4668 

4906 

5 o 44 

5131 

5219 

5307 

53g4 

88 

496 

5482 

5569 

6607 

3744 

5832 

5919 

6007 

6094 

6182 

6269 

87 

497 

6356 

6444 

6531 

6618 

16706 

6 79 3 

63So 

6968 

70OO 

7142 

87 

498 

7229 

7817 

7404 

7491 

7578 

7660 

77 52 

7839 

7926 

8014 

87 

499 

8101 

8188 

8275 

8362 

8449 

8535 

8622 

8709 

8796 

8883 

87 

5oo 

698970 

9 o 5 7 

9144 

9231 

9317 

94o4 

949 1 

9 5 7 8 

9664 

975 i 

87 

5oi 

9 338 

9924 

®*u 

**98 

•184 

®27I 

®358 

•444 

•531 

°6i7 

87 

502 

700704 

0790 

0877 

0963 

io 5 o 

1136 

1222 

1309 

i 3 9 5 

1482 

86 

5o3 

1568 

1604 

1741 

1827 

1913 

1999 

20S6 

2172 

2208 

2344 

86 

5 04 

2431 

2517 

26o3 

2689 

2 77 5 

2861 

2947 

3o33 

3 I ! 9 

32 o 5 

86 

5o5 

3291 

3377 

3463 

3549 

3635 

3721 

3807 

38 9 3 

3979 

4 o 65 

86 

5o6 

4161 

4236 

4322 

4408 

4494 

4079 

4660 

4761 

4837 

4922 

86 

5 oj 

5oo8 

6094 

6179 

5265 

535o 

5436 

5522 

5607 

5698 

5778 

86 

5o8 

5864 

5949 

6o35 

6120 

6206 

6291 

6376 

6462 

6547 

6632 

85 

509 

6718 

68o3 

6888 

6974 

7°5 9 

7144 

7229 

7315 

7400 

7485 

85 

5io 

707670 

7655 

7740 

7826 

7911 

7996 

8081 

8166 

0251 

8336 

85 

5i i 

8421 

85o6 

8591 

8676 

8761 

8846 

8931 

9015 

9100 

9185 

85 

512 

9270 

9355 

9440 

9824 

9609 

9694 

9779 

9 863 

9948 

c ®33 

85 

513 

710117 

0202 

0287 

0371 

0456 

o54o 

0625 

0710 

0794 

0870 

85 

5 i 4 

096^ 

1048 

1132 

1217 

13o 1 

1385 

1470 

1004 

1689 

1728 

84 

515 

1807 

1892 

1976 

2060 

2i44 

2229 

2313 

2397 

2481 

2566 

84 

516 

265c 

2734 

2818 

2902 

2986 

3070 

3154 

3238 

3323 

3407 

84 

517 

3491 

3575 

3609 

3742 

3826 

3910 

3994 

4078 

4162 

4246 

84 

518 

433c 

44i4 

4497 

4581 

4665 

4749 

4833 

4916 

5ooo 

6084 

84 

619 

8167 

020 j 

5335 

6418 

55o2 

5586 

5669 

5753 

5836 

5920 

84 

N. 

0 

1 

2 

3 

4 

5 

6 

1 7 

8 

9 

D. 
















































































A TABLE OF LOGARITHMS FROM 1 TO 10,000 


9 


N. 

O 

1 

2 

3 

4 

5 

6 

7 

8 | 

1 

9 

D. 

520 

7l6003 

6087 

6170 

6254 

633 7 

6421 

65 o 4 

6588 

6671 

6754 

83 

521 

6838 

6921 

7004 

7088 

7171 

7254 

7338 

7421 

75o4 

7 58 7 

83 

522 

7671 

7734 

7837 

7920 

8oo3 

8086 

8169 

8253 

8336 

8419 

83 

523 

85 o 2 

8585 

8668 

8761 

8834 

89 1 7 

9000 

9083 

9166 

9248 

83 

524 

g331 

9414 

9497 

9680 

9663 

9743 

9828 

9911 

9994 

®*77 

83 

525 

720169 

0242 

o 325 

0407 

0490 

0873 

o655 

0738 

0821 

0903 

83 

526 

0986 

1068 

1151 

1288 

1316 

1398 

1481 

1563 

1646 

1728 

82 

527 

1811 

1893 

i 97 5 

2 o 58 

2140 

2222 

23 o 5 

2387 

2469 

2552 

*82 

528 

2634 

2716 

2798 

2881 

2963 

3o45 

3127 

3209 

3291 

3374 

82 

529 

3456 

3538 

3020 

3702 

3784 

3866 

3948 

4 o 3 o 

4112 

4194 

82 

53o 

724276 

4358 

4440 

4522 

4604 

4685 

4767 

4849 

4931 

5oi3 

82 

531 

5og5 

6176 

5258 

5340 

5422 

55o3 

5585 

5667 

5748 

583o 

82 

532 

6912 

5993 

6075 

6156 

6238 

6320 

6401 

6483 

6564 

6646 

82 

533 

6727 

6809 

6890 

6972 

7o53 

7184 

7216 

7297 

7 3 79 

7460 

81 

534 

7641 

7623 

7704 

778D 

7866 

7948 

8029 

8110 

8191 

8273 

81 

535 

8354 

8435 

8016 

8097 

8678 

8709 

8841 

8922 

9003 

9084 

81 

536 

9165 

9246 

9827 

9408 

9489 

967° 

9&5 i 

9782 

9813 

9893 

81 

53 7 

9974 

**55 

®i36 

*217 

*298 

0878 

*489 

®54o 

•621 

*702 

81 

538 

730782 

o863 

0944 

1024 

1 io5 

1186 

1266 

1347 

1428 

i5o8 

81 

53 9 

1589 

1669 

1760 

i83o 

1911 

1991 

2072 

2152 

2233 

2313 

81 

54o 

732394 

2474 

2555 

2635 

2716 

2796 

2876 

2g56 

3 o 37 

3117 

80 

541 

3197 

3278 

3358 

3438 

3518 

3598 

3679 

3759 

383 9 

3919 

80 

542 

3999 

4079 

4160 

4240 

4320 

4400 

4480 

456o 

4640 

4720 

80 

543 

4800 

4880 

4960 

6040 

5l20 

5200 

5279 

5359 

6439 

5519 

80 

544 

5599 

6679 

D709 

5838 

5918 

5998 

6078 

6167 

6237 

6317 

80 

545 

6397 

6476 

6556 

6635 

67 x 5 

6795 

6874 

6964 

7034 

7113 

80 

546 

7193 

7272 

7352 

7431 

7611 

7090 

7670 

7749 

7829 

7908 

79 

547 

7987 

8067 

8146 

8226 

83o5 

8384 

8463 

8 o 43 

8622 

8701 

79 

548 

8781 

8860 

8989 

9018 

9097 

9177 

9256 

9335 

9414 

9493 

79 

549 

9072 

9661 

9 7 3 i 

9810 

9889 

9968 

o® 4 7 

® 1 26 

®2 o 5 

*284 

79 

55o 

74 o 363 

0442 

o 52I 

0600 

0678 

0757 

o836 

0915 

0994 

1073 

79 

55x 

I 152 

I 23 o 

1309 

i388 

1467 

1846 

1624 

1703 

1782 

i860 

79 

552 

1939 

2018 

2096 

2176 

2254 

2332 

2411 

2489 

2568 

2647 

79 

553 

2726 

2804 

2882 

2961 

3o3g 

3i 18 

3196 

3276 

3353 

343i 

78 

554 

35io 

3588 

3667 

3749 

3823 

3902 

3980 

4 o 58 

4136 

4215 

78 

555 

4293 

4371 

4449 

4528 

4606 

4684 

4762 

4840 

4919 

4997 

78 

556 

5oj5 

5153 

523 x 

53 o 9 

5387 

5465 

5543 

5621 

5699 

5777 

78 

557 

5855 

5 9 33 

6011 

6089 

6167 

6245 

6323 

6401 

6479 

6556 

78 

558 

6634 

6712 

6790 

6868 

6945 

7023 

7101 

7 1 79 

7256 

7334 

78 

559 

7412 

7489 

7567 

7649 

7722 

7800 

7878 

7955 

8o33 

8110 

78 

56o 

748188 

8266 

8343 

8421 

8498 

8876 

8653 

873 i 

8808 

8885 

77 

561 

8963 

9040 

9118 

9! 9 0 

9272 

935o 

9427 

9604 

9682 

9669 

77 

562 

9736 

9814 

9891 

9968 

°®40 

® I 23 

*200 

•277 

*354 

•43 i 

77 

563 

-]5o5oS 

o586 

o663 

0740 

0817 

0894 

°971 

1048 

1125 

1202 

77 

564 

1279 

1356 

1433 

i5io 

1587 

1664 

1741 

1818 

1895 

1972 

77 

565 

2048 

2125 

2202 

2279 

2356 

2433 

2809 

2586 

2663 

2740 

77 

566 

2816 

2893 

2970 

3o47 

3123 

3200 

3277 

3353 

343o 

35o6 

77 

567 

3583 

366o 

3786 

3813 

3889 

3966 

4042 

4i 19 

4198 

4272 

77 

568 

4348 

4425 

45 oi 

4578 

4654 

4730 

4807 

4883 

4960 

5o36 

76 

669 

5112 

5189 

5265 

5341 

5417 

5494 

5570 

5646 

5722 

5799 

76 

570 

755876 

5951 

6027 

6io3 

6180 

6256 

6332 

6408 

6484 

656o 

76 

571 

6636 

6712 

6788 

6864 

6940 

7016 

7092 

7168 

7244 

7320 

76 

572 

73 q 6 

7472 

7648 

7624 

7700 

7775 

7851 

7927 

8oo3 

8079 

76 

673 

81551 823 o 

83 06 

8382 

8458 

8533 

8609 

8685 

8761 

8836 

76 

674 

8912 8988 

9063 

9 i3 9 

9214 

9290 

9366 

9441 

9017 

9692 

76 

575 

0668 

. 9743 

9819 

9894 

9970 

®®45 

0 121 

®ig6 

*272 

•347 

75 

576 

760422 0498 

0678 

0649 

0724 

°799 

0878 

0900 

1025 

1101 


577 

1176 

I 251 

1326 

1402 

1477 

1532 

1627 

1702 

1778 

1853 

7^ 

578 

1928 

2003 

2078 

2153 

2228 

23 o 3 

2378 

2453 

2629 

2604 

75 

579 

2679 

2754 

1 

2829 

2904 

2978 

3o53 

3n8 

32 o 3 

3278 

3353 

7 5 

N. 

0 

. 

1 

2 

1 

3 

4 

5 

6 

7 

8 

9 

D. 
























































10 A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. 

0 

1 

2 

3 

4 

1 5 

6 

7 

j 8 

9 

D. 

58o 

76342E 

35o3 

3578 

3653 

3727 

38 o 2 

3877 

3 9 52 

4027 

4101 

75 

581 

417^ 

425 i 

4326 

44oo 

4475 

455 o 

4624 

4699 

4774 

4848 

75 

582 

492: 

4998 

5072 

5147 

5221 

5296 

5370 

5445 

5520 

55 9 4 

75 

583 

566$ 

5743 

5818 

58 9 2 

6966 

6041 

6115 

6190 

6264 

6338 

74 

584 

64i3 

6487 

6562 

6636 

6710 

6785 

685 9 

6 9 33 

7007 

7082 

74 

585 

7156 

7230 

73o4 

7379 

7453 

7527 

7601 

7675 

7749 

7823 

74 

586 

7898 

7972 

8046 

8x20 

8194 

8268 

8342 

8416 

8490 

8564 

74 

58 7 

8638 

8712 

8786 

8860 

8 9 34 

9008 

9082 

9 x 56 

9280 

9 3 o 3 

74 

588 

9377 

940 1 

9 525 

9 5 99 

9673 

9746 

9820 

9894 

9968 

e®42 

74 

589 

770115 

0189 

0263 

o336 

04x0 

0484 

0557 

o63i 

0706 

0778 

74 

5 9 o 

770832 

0926 

oggg 

1073 

1146 

1220 

1293 

1367 

1440 

i 5 i 4 

74 

5 9 X 

1587 

1661 

1734 

1808 

1881 

i 9 55 

2028 

2102 

2176 

2248 

7 3 

5 9 2 

2322 

23 9 5 

2468 

2542 

2615 

2688 

2762 

2835 

2908 

2981 

7 3 

5 9 3 

3o55 

3128 

3201 

3274 

3348 

3421 

3494 

3567 

364o 

3~ii3 

7 3 

5 9 4 

3786 

386o 

3 9 33 

4006 

4079 

4i 52 

4225 

4298 

4371 

4444 

7 3 

5 9 d 

45i7 

45 9 o 

4663 

4736 

4809 

4882 

4 9 55 

5 o 2 8 

5ioo 

5173 

7 3 

5 9 6 

5246 

53 i 9 

53 9 2 

5465 

5538 

56io 

5683 

6756 

582 9 

5 9 02 

7 3 

5 Q1 

5974 

6047 

6120 

6 i 9 3 

6265 

6338 

641 X 

6483 

6556 

6629 

73 

5gS 

6701 

6774 

6846 

6919 

6992 

7064 

7137 

7209 

7282 

7354 

73 

5 99 

7427 

7499 

7672 

7644 

7717 

7789 

7862 

7934 

8006 

8079 

72 

600 

778161 

8224 

8296 

8368 

8441 

85i3 

8585 

8658 

8730 

8802 

72 

601 

8874 

8947 

9 OI 9 

9°9 I 

9 i 63 

9236 

9 3o8 

9 38 o 

9452 

9524 

72 

602 

g5g6 

9669 

974i 

9 8 i 3 

9 883 

9957 

®«2 9 

®ioi 

*173 

®245 

72 

6o3 

780317 

o 38 9 

046 X 

o533 

o6o5 

0677 

0749 

0821 

o8 9 3 

o 9 65 

72 

604 

io3~i 

1109 

1181 

1253 

i 324 

i 3 9 6 

1468 

1540 

1612 

1684 

72 

6o5 

i 7 55 

1827 

lS 99 

I 97 I 

2042 

2114 

2186 

2258 

2329 

2401 

72 

606 

2473 

2544 

2616 

2688 

2 7 5 9 

2831 

2902 

2974 

8046 

3117 

72 

607 

3 i 8 9 

3260 

3332 

34o3 

3473 

3546 

36i8 

368o 

3761 

3832 

7i 

608 

3 9 o 4 

3975 

4046 

4118 

4189 

4261 

4332 

44 o 3 

4475 

4546 

71 

609 

4617 

4689 

4760 

4831 

4902 

4974 

5 o 45 

5 i 16 

5187 

525g 

7* 

610 

78533 o 

54 oi 

5472 

5543 

5615 

5686 

6757 

5828 

58 qq 

5gj° 

71 

611 

6041 

6112 

6x83 

6254 

6325 

6896 

6467 

6538 

6609 

6680 

7 1 

612 

6761 

6822 

68 9 3 

6964 

7o35 

7106 

7177 

7248 

7319 

7390 

71! 

6x3 

7460 

753 i 

7602 

7673 

7744 

7816 

7885 

7 9 56 

8027 

8098 

71 

614 

8168 

8239 

8310 

8381 

8451 

8522 

85 9 3 

8663 

8734 

8804 

71 

615 

88 7 5 

8946 

9016 

9087 

9157 

9228 

9299 

9 36 9 

9440 

9 5 io 

71 

616 

9681 

9 651 

9722 

9792 

9 863 

9933 

O©©/ 

°®74 

®*44 

®2l5 

70 

617 

790285 

o356 

0426 

0496 

0567 

0637 

0707 

0778 

0848 

0918 

7° 

618 

0988 

io 5 9 

1129 

1 x 99 

1269 

1340 

1410 

1480 

1030 

1620 

70 

619 

1691 

1761 

i 83 i 

1901 

1971 

2041 

211 X 

2181 

2252 

2322 

70 

620 

792392 

2462 

2532 

2602 

2672 

2742 

2812 

2882 

2 9 52 

3022 

70 

621 

3 o 9 2 

3 i 62 

323 x 

33oi 

33 7 i 

3441 

35i 1 

358i 

365i 

3 9 2I 

70 

622 

3790 

3 860 

3 9 3 o 

4000 

4070 

4139 

4209 

4279 

4349 

44l8 

7° 

623 

4488 

4558 

4627 

4697 

4767 

4836 

4906 

4976 

5040 

5n5 

7° 

624 

5i85 

5254 

5324 

53 9 3 

5463 

5532 

56 o 2 

5672 

5741 

58n 

70 

625 

588o 

5949 

6019 

6088 

6158 

6227 

6297 

6366 

6436 

65o5 

69 

626 

6574 

6644 

6713 

6782 

6852 

6921 

6990 

7060 

7 I2 9 

7198 

69 

627 

7268 

7337 

74o6 

7475 

7545 

7614 

7683 

7762 

7821 

7890 

69 

628 

7960 

8029 

8098 

8167 

8236 

83o5 

8374 

8443 

85x3 

8582 

69 

629 

8651 

8720 

8789 

8858 

8927 

8996 

9 o 65 

9 i 34 

9 2o3 

9272 

69 

63o 

799341 

9409 

9478 

9547 

9616 

9 685 

9754 

9823 

9892 

9961 

69 

631 

800029 

0098 

0167 

0236 

o3o5 

0373 

0442 

o5i 1 

o58o 

0648 

69 

632 

0717 

0786 

0854 

0923 

0992 

1061 

1129 

1198 

1266 

i335 

69 

633 

i4o4i 

1472 

1541 

1609 

1678 

1747 

i 8 i 5 

1884 

1962 

2021 

69 

634 

2089 

2158 

2226 

2290 

2363 

2432 

25 oo 

2568 

2W7 

2705 

69 

635 

2774 

2842 

2910 

2979 

3 047 

31 x6 

3 i 84 

3252 

3321 

338 9 

68 

636 

3457 

3525 

35 9 4 

3662 

3-]3o 

3798 

3867 

3 9 35 

4 oo 3 

4071 

68 

63~] 

4139 

4208 

4276 

4344 

4412 

4480 

4548 

4616 

4685 

4753 

68 

638 

4821 

4889 

4957 

5o25 

5o 9 3 

5i6i 

5229 

6297 

5365 

5433 

68 

63 9 

55oi 

556 9 

5637 

6706 

5 77 3 

584 i 

5 9 o 8 

5976 1 

6044 

6112 

68 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 1 

9 

D. 






















































































A TABLE OF LOGARITHMS FROM 1 TO 10,000. 11 


N. 

0 

1 

2 

3 

4 

5 

1 6 

7 

8 

9 

D. 

640 

806180 

6248 

6316 

6384 

645 i 

6519 

658 7 

6655 

6723 

6790 

68 

641 

6858 

6926 

6994 

7061 

7129 

7i97 

7264 

7332 

7400 

7467 

68 

642 

7535 

7603 

7670 

7 7 38 

7806 

7873 

7941 

8008 

8076 

8148 

68 

643 

8211 

8279 

8346 

8414 

8481 

8549 

86x6 

8684 

8781 

8818 

67 

644 

8886 

8 9 53 

9021 

9088 

9156 

9223 

9290 

9 358 

9425 

9492 

67 

645 

9560 

9627 

9694 

9762 

9829 

9896 

9964 

®®3i 

••98 

•165 

67 

646 

8 io 233 

o3oo 

0367 

0434 

o5oi 

0569 

o636 

0703 

0770 

0837 

67 

647 

0904 

0971 

1039 

XI06 

1173 

1240 

1307 

i 3 7 4 

1441 

i 5 o 8 

67 

648 

1675 

1642 

1709 

1776 

1843 

1910 

1977 

2044 

2111 

2178 

67 

649 

2245 

2312 

23 79 

2445 

2512 

25 79 

2646 

2713 

2780 

2847 

67 

65o 

812913 

2980 

3o47 

3 ii 4 

3181 

3247 

3314 

338i 

3448 

35x4 

67 

651 

358i 

3648 

3714 

3781 

3848 

3914 

3981 

4048 

4114 

4181 

67 

652 

4248 

4314 

438 i 

4447 

45 i 4 

458 i 

4647 

4714 

4780 

4847 

67 

653 

4913 

4980 

6046 

5113 

5179 

5246 

5312 

53 7 8 

5445 

55i 1 

66 

654 

5578 

5644 

5711 

5777 

5843 

6910 

5976 

6042 

6109 

6175 

66 

655 

6241 

63o8 

6374 

644o 

65o6 

65 7 3 

6639 

6706 

6771 

6838 

66 

656 

6904 

6970 

7036 

7102 

7169 

7235 

7 3 oi 

7367 

7433 

7499 

66 

65-] 

7565 

763 i 

7698 

7764 

7830 

7896 

7962 

8028 

8094 

8160 

66 

658 

8226 

8292 

83 d 8 

8424 

8490 

8556 

8622 

8688 

8754 

8820 

66 

669 

8885 

8961 

9 OI 7 

9083 

9149 

92i5 

9281 

9346 

9412 

9478 

66 

660 

819544 

9610 

9676 

9741 

9807 

9873 

99 3 9 

©OO/ 

4 

0070 

• 136 

66 

661 

820201 

0267 

o333 

0399 

0464 

o53o 

0696 

0661 

0727 

0792 

66 

662 

o858 

0924 

0989 

JODO 

1X20 

1186 

I25l 

1317 

i 382 

1448 

66 

663- 

1514 

15 79 

1645 

17IO 

1775 

1841 

1906 

1972 

2 o 3 7 

2103 

65 

664 

2168 

2233 

2299 

2864 

2430 

24g5 

256o 

2626 

2691 

2756 

65 

665 

2822 

2887 

2962 

3oi8 

3o83 

3148 

3 213 

3279 

3344 

3409 

65 

666 

3474 

3539 

36o5 

3670 

3-j35 

3 800 

3865 

3o3o 

3996 

4061 

65 

667 

4126 

4191 

4256 

4321 

4386 

4451 

45 i 6 

4081 

4646 

4711 

65 

668 

4776 

4841 

4906 

4971 

5o36 

5xoi 

5x66 

0231 

5296 

536i 

65 

669 

5426 

5491 

5556 

5621 

5686 

5~j5i 

58x5 

588o 

5945 

6010 

65 

670 

826075 

6140 

6204 

6269 

6334 

63gg 

6464 

6628 

65 9 3 

6658 

65 

67 1 

6723 

6787 

6852 

6917 

6981 

7046 

7111 

7n5 

7240 

i 3 o 5 

65 

672 

7369 

7434 

7499 

7 563 

7628 

7692 

7757 

7821 

7886 

7951 

65 

673 

8oi5 

8080 

8144 

8209 

8273 

8338 

8402 

8467 

8531 

8095 

64 

674 

8660 

8724 

8789 

8853 

8918 

8982 

9046 

9111 

9 J 7 5 

9289 

64 

676 

9304 

9 368 

9432 

9497 

9661 

9625 

9690 

9754 

9818 

9882 

64 

676 

9947 

eon 

e* 7 5 

® 139 

•204 

•268 

®332 

*896 

®46o 

•525 

64 

677 

83 o 589 

o653 

0717 

0781 

0845 

0909 

0973 

1087 

1102 

1166 

64 

678 

I23 o 

1294 

1358 

1422 

i486 

x55o 

1614 

1678 

1742 

1806 

64 

679 

1870 

1934 

1998 

2062 

2126 

2189 

2253 

23x7 

238 i 

2445 

64 

680 

8325 o 9 

25-]3 

2637 

2700 

2764 

2828 

2892 

2956 

3020 

3o83 

64 

681 

3 i 47 

3211 

3275 

3338 

3402 

3466 

3530 

3098 

3657 

3721 

64 

682 

3784 

3848 

3912 

397D 

4039 

4 io 3 

4166 

4280 

4294 

4357 

64 

683 

4421 

4484 

4548 

4611 

4675 

4739 

4802 

4866 

4929 

4993 

64 

684 

5o56 

5l20 

5x83 

5247 

5310 

53 7 3 

5437 

55oo 

5564 

5627 

63 

685 

5691 

5754 

5817 

5881 

5 9 44 

6007 

6071 

6 i 34 

6197 

6261 

63 

686 

6324 

6387 

645 i 

6514 

6577 

6641 

6704 

6767 

683o 

6894 

63 

687 

6957 

7020 

7 o83 

7x46 

7210 

7273 

7 336 

7399 

7462 

7525 

63 

688 

7588 

7602 

77x5 

7778 

7841 

79°4 

7967 

8 o 3 o 

8093 

8x56 

63 

689 

8219 

8282 

8345 

8408 

8471 

8534 

8597 

8660 

8723 

8786 

63 

690 

838849 

8912 

8975 

9038 

9101 

9164 

9^7 

9280 

9352 

9415 

63 

691 

9478 

9541 

9604 

9667 

9729 

9792 

9853 

9918 

9981 

®®43 

63 

692 

840106| 

0169 

0232 

0294 

0357 

0420 

0482 

o 545 

0608 

0671 

63 

698 

0733I 

0796 

0869 

0921 

0984 

1046 

1109 

1172 

1234 

1297 

63 

694 

l35q' 

1422 

1485 

1547 

1610 

1672 

1735 

1797 

i860 

1922 

63 

695 

1985 

2047 

2IIO 

2172 

2235 

2297 

236o 

2422 

2484 

2547 

62 

696 

2609 

2672 

2734 

2796 

2859 

2921 

2983 

3046 

3108 

3170 

62 

697 

3233 

3295 

3357 

3420 

3482 

3544 

36o6 

3669 

3-]3i 

3793 

62 

698 

3855* 

3oi8 

3980 

4042 

4104 

4166 

4229 

4291 

/,353 

44i 5 

62 

699 

4477 

4539 

46oi 

4664 

4726 

4788 

485 o 

4912 

4974 

5o36 

62 

N. 

0 

1 

2 1 

3 

4 

5 

6 1 

7 

8 

9 

D 







































































12 A TABLE OF LOGARITHMS FROM 1 TO 10 , 000 . 


N. 

0 

I 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

700 

840098 

5 160 

5222 

5284 

5346 

5408 

5470 

5532 

5594 

1 5656 

62 

701 

5718 

5780 

5842 

8904 

6966 

.6028 

6090 

61 5 1 

621 3 

1 6273 

62 

702 

633 7 

6399 

6461 

6523 

6585 

6646 

6708 

6770 

6832 

6894 

62 

703 

6933 

7017 

7°79 

7141 

7202 

7264 

7326 

7 3 88 

7449 

75 1 1 

62 

704 

7 5 7 3 

7634 

7696 

7738 

7819 

7881 

79 4 3 

8004 

8066 

8128 

62 

703 

8189 

8231 

83 12 

8374 

8435 

8497 

8559 

8620 

8682 

8743 

62 

706 

88 o 5 

8866 

8928 

8989 

9061 

9112 

9 1 74 

9235 

9297 

9358 

61 

707 

9419 

9481 

9342 

9604 

9863 

9726 

9788 

9849 

99 " 

9972 

61 

708 

85 oo 33 

oog 5 

01 56 

0217 

0279 

o34o 

0401 

0462 

0324 

o 585 

61 

709 

0646 

0707 

0769 

o 83 o 

0891 

0962 

1014 

1075 

1 1 36 

"97 

61 

710 

85 i 238 

1320 

1 38 1 

1442 

i 5 o 3 

1 564 

, 1625 

1686 

1747 

1809 

61 

711 

1870 

iq3i 

1992 

2 o 53 

2114 

2175 

2236 

2297 

2358 

2419 

61 

712 

2480 

2641 

2602 

2663 

2724 

2785 

2846 

2907 

2968 

3029 

61 

713 

3 ogo 

3 i 5 o 

3211 

3272 

3333 

3394 

3455 

35 16 

3377 

3637 

61 

7 i 4 

3698 

3739 

3820 

388 i 

3941 

4002 

4o63 

4124 

4 1 85 

4245 

61 

710 

43 o 6 

4367 

4428 

4488 

4549 

4610 

4670 

473i 

4792 

4852 

61 

716 

49'3 

4974 

5o34 

5093 

5 i 56 

52 i 6 

5277 

5337 

53 ,s 

5439 

61 

7*7 

5319 

558 o 

5640 

5701 

5761 

5822 

5882 

5943 

6 oo 3 

6064 

61 

718 

6124 

61 85 

6245 

63 06 

6366 

6427 

6487 

6548 

6608 

666S 

60 

719 

6729 

6789 

685 o 

6910 

6970 

7031 

7091 

71 52 

7212 

7272 

60 

720 

837332 

7 3 9 3 

7453 

751 3 

7^74 

7634 

7694 

7755 

73 1 5 

7875 

60 

721 

79 33 

7995 

8 o 56 

8116 

8176 

8236 

8297 

8357 

8417 

8477 

60 

722 

8537 

8397 

8667 

8718 

8778 

8833 

8898 

8 9 58 

9018 

9078 

60 

723 

91 38 

9 '98 

9208 

9 3i8 

9 3 79 

9439 

9499 

9069 

9619 

9679- 

60 

724 

97 3 9 

9799 

9869 

9918 

9978 

°®38 

**98 

°i 58 

•218 

•278 

60 

723 

86 o 338 

0398 

0458 

o 5 i 8 

0578 

o 63 7 

0697 

0767 

0817 

0877 

60 

726 

oq37 

0996 

1036 

1116 

1176 

1 236 

1290 

1 355 

1416 

1473 

■6o 

727 

1 534 

1694 

1664 

1714 

1773 

1 833 

1893 

1952 

2012 

2072 

60 

728 

21 3 1 

2191 

2231 

23io 

2370 

243 o 

2489 

2349 

2608 

2668 

60 

729 

2728 

2787 

2847 

2906 

2966 

3o25 

3 o 85 

3 1 44 

32o4 

3263 

60 

73 o 

863323 

3332 

3442 

35 oi 

3 56 1 

3620 

363 o 

3739 

3799 

3858 

5 9 

7 31 

3917 

3977 

4 o 36 

4096 

4 1 55 

4214 

4274 

4333 

4392 

4432 

5 9 

7 3 2 

431 1 

4370 

463 0 

4689 

4748 

4808 

4867 

4926 


5 o 43 

5 9 

733 

5 104 

5 1 63 

5222 

5282 

534i 

5400 

5469 

55 i 9 

5578 

5637 

5 9 

734 

5696 

5735 

5 y 14 

58 7 4 

5 9 33 

6992 

6 o 5 r 

6110 

6169 

6228 

5 9 

735 

6287 

6346 

6405 

6466 

6524 

6583 

6642 

6701 

6760 

6819 

59 

736 

6878 

6937 

6996 

7033 

7114 

7173 

7232 

7291 

7350 

7409 

5 9 

7 3 7 

7467 

7626 

7083 

7644 

77 ° 3 

7762 

7821 

7880 

7989 

7998 

5 9 

7 38 

8 o 56 

811 5 

8174 

8233 

8292 

835 o 

8409 

8468 

8327 

8586 

39 

7 3 9 

8644 

8703 

8762 

8821 

8879 

8 9 33 

8997 

9056 

9114 

9173 

5 9 

740 

869232 

9290 

9349 

9408 

9466 

9525 

9534 

9642 

9701 

9760 

5 9 

74 i 

9818 

9 S 77 

9935 

9994 

*®53 

®i 11 

*170 

®22S 

*287 

®345 

5 2 

742 

870404 

0462 

0321 

0379 

o 638 

0696 

0755 

oSi 3 

0872 

0930 

58 

743 

0989 

1047 

1 106 

1164 

1223 

1281 

1 339 

i 3 o 8 

1456 

1313 

58 

744 

1673 

1 63 1 

1690 

1748 

1806 

1 865 

' 9 23 

1981 

2040 

2098 

58 

745 

21 56 

221 5 

2273 

233 1 

2389 

2448 

25o6 

2564 

2622 

2681 

58 

746 

27 3 9 

2 797 

2855 

2913 

2972 

3 o 3 o 

3o88 

3i46 

3204 

3262 

58 

747 

3321 

33 79 

3437 

3495 

3553 

36 11 

3669 

2727 

3785 

3844 

58 

748 

3902 

3960 

4018 

4076 

4 1 34 

4192 

425 o 

43 o 8 

4366 

4424 

58 

749 

4482 

4640 

4698 

4656 

4714 

4772 

483o 

4888 

4 y 43 

5 oo 3 

58 

760 

876061 

5 119 

5 1 77 

5235 

6293 

535 1 

5409 

5466 

5524 

5582 

58 

731 

564 o 

6698 

5706 

58 1 3 

58 7 i 

5929 

5987 

6045 

6102 

6160 

58 

732 

6218 

6276 

6333 

6391 

6449 

6507 

6564 

6622 

6680 | 

6737 

58 

753 

6793 

6853 

6910 

6968 

7026 

7083 

7141 

7*99 

7256 } 

7314 

58 

754 

7 3 7 i 

7429 

7487 

7544 

7602 

7639 

77'7 

7774 

7832 1 

78S9 

58 

733 

7947 

8004 

8062, 

8119 

8177 

8234 

8292 

8349 

8407 I 

8464 

57 

736 

8522 

8579 

8087 

8694 

8762 

8809 

8866 ' 

8924 

8981 ; 

9339 

57 

7 5 7 

9096 

9 i 53 

9211 

9268 

9 3 23 

9333 

9440 

9497 

9333 1 

9612 

57 

758 

9669 

9726 

9784 

9841 

9898 

9906 

® 8 i 3 

°® 7 0 

0,27 

©183 

57 

739 

880242 

0299 

o 356 

041 3 

0471 

o528 

o 585 

0642 

0699 j 

0756 

57 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 








































































A TABLE OF LOGARITHMS FROM 1 TO 10,000. 13 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

760 

8808i' 

0871 

0928 

0985 

1042 

1099 

1156 

1213 

1271 

1328 

57 

761 

138c 

*442 

1499 

1556 

1613 

1670 

1 1' 2 1 

1784 

1841 

1898 

57 

762 

195: 

2012 

2069 

2126 

2183 

2240 

2297 

2354 

2411 

2468 

57 

763 

232; 

2581 

2638 

2696 

2752 

2809 

2866 

2923 

2980 

3 037 

57 

764 

809, 

3 i5o 

3207 

3264 

3321 

3377 

3434 

3491 

3548 

36o5 

57 

760 

3661 

3718 

3 77 5 

3832 

3888 

3945 

4002 

4039 

4* i5 

4*72 

57 

766 

422<; 

4285 

4342 

4399 

4455 

4612 

4669 

4623 

4682 

4739 

57 

767 

4792 

4852 

490Q 

4965 

5022 

6078 

5135 

5192 

5248 

53o5 

57 

768 

5361 

54*8 

5474 

5531 

5587 

5644 

5700 

5 7 5 7 

58(3 

5870 

57 

769 

5926 

5988 

6089 

6096 

6i52 

6209 

6265 

6321 

63 7 8 

6434 

56 

770 

886491 

6547 

6604 

6660 

6716 

6773 

6829 

6885 

6942 

6998 

56 

77i 

7034 

71 * 1 

7167 

7223 

7280 

7336 

7 3 9 2 

7449 

7303 

7361 

56 

772 

7617 

7674 

773o 

7786 

7842 

7898 

7933 

8011 

8067 

8123 

56 

773 

8179 

8236 

8292 

8348 

8404 

8460 

8516 

85 ~ i 3 

8629 

8685 

56 

774 

8741 

8797 

8853 

8909 

8966 

9021 

9°77 

9*34 

9190 

9246 

56 

773 

9302 

9358 

94*4 

9470 

9626 

9682 

9 638 

9694 

973° 

9806 

56 

776 

9862 

9918 

9974 

°*3o 

o®86 

®i4* 

®*97 

»253 

*309 

•365 

56 

777 

890421 

0477 

o533 

o589 

0645 

0700 

0766 

0812 

0868 

0924 

56 

77« 

0980 

io35 

1091 

1147 

1203 

1259 

1314 

1370 

1426 

1482 

56 

779 

i53 7 

1593 

1649 

1705 

1760 

1816 

1872 

192S 

1983 

2039 

56 

780 

892095 

2i5o 

2206 

2262 

2317 

23-]3 

2429 

2484 

2640 

2595 

56 

781 

2651 

2707 

2762 

2818 

2873 

2Q29 

2983 

3o4o 

3096 

3151 

56 

782 

3207 

3262 

3318 

33 7 3 

3429 

3484 

334o 

3595 

3651 

8706 

56 

78 3 

3762 

3817 

38 7 3 

3928 

3984 

4039 

4094 

4*5o 

42o5 

4261 

55 

784 

4316 

4371 

4427 

4482 

4538 

45g3 

4648 

4704 

4739 

4814 

55 

785 

4870 

4925 

4980 

5o36 

5091 

5146 

5201 

5267 

5312 

5367 

55 

786 

5423 

5478 

5o33 

5588 

5644 

6699 

3734 

5809 

5864 

5920 

55 

787 

5975 

6o3o 

6o85 

6140 

6195 

6261 

63o6 

6361 

6416 

6471 

55 

788 

6526 

6581 

6636 

6692 

6747 

6802 

6867 

6912 

6967 

7022 

55 

789 

7077 

7i32 

7*87 

7242 

7297 

7352 

7407 

7462 

7317 

7572 

55 

790 

897627 

7682 

7737 

779 2 

7847 

7902 

79 5 7 

8012 

8067 

8122 

55 

79i 

8176 

823i 

8286 

834* 

83g6 

845i 

8006 

8561 

86(5 

8670 

55 

792 

8726 

8780 

8835 

8890 

8944 

8999 

9054 

9*°9 

9164 

9218 

55 

7 9 3 

9273 

9328 

g383 

9437 

9492 

954.7 

9602 

9636 

9711 

9766 

55 

79^ 

9821 

9875 

9930 

9980 

0*39 

eo g 4 

°i49 

®2o3 

•258 

®312 

55 

19 ° 

900367 

0422 

0476 

oo3* 

o586 

0640 

o6g5 

0749 

0804 

o85g 

55 

796 

0913 

0968 

1022 

1077 

1131 

Il86 

1240 

1293 

*349 

1404 

55 

797 

1458 

1513 

i 56 j 

1622 

1676 

1731 

1785 

1840 

1894 

1948 

54 

• 798 

2003 

2057 

2112 

2166 

2221 

22 7 0 

2329 

2384 

2438 

2492 

54 

799 

2547 

2601 

2655 

2710 

2764 

2818 

2873 

2927 

2981 

3o36 

54 

Boo 

903090 

3144 

3*99 

3253 

33o7 

336i 

34i6 

3470 

3524 

3378 

54 

Bo 1 

3633 

3687 

3741 

3795 

3849 

3904 

3968 

4012 

4066 

4*20 

54 

Bo2 

4*74 

4229 

4283 

4337 

4391 

4443 

4499 

4553 

4607 

4661 

54 

Bo3 

47*6 

4770 

4824 

4878 

4932 

4986 

5o4o 

5094 

5i48 

5202 

54 

804 

52561 

53io 

5364 

5418 

5472 

5026 

558o 

5634 

5688 

5742 

54 

8o5 

5796 

585o 

6904 

5 9 5S 

6012 

6066 

6119 

6173 

6227 

6281 

54 

806 

6335 

638 9 

6443 

6497 

6551 

66o4 

6658 

6712 

6766 

6820 

54 

807 

6874 

6927 

6981 

7033 

7089 

7*43 

7*96 

725o 

7804 

7358 

54 

808 

74* * 

7465 

7019 

7 5 7 3 

7626 

7680 

7734 

7787 

784* 

7895 

54 

809 

7949 

8002 

8o56 

8110 

8163 

8217 

8270 

8324 

83 7 8 

843i 

54 

810 

908485 

8539 

8592 

8646 

8699 

8753 

8807 

8860 

89*4 

8967 

54 

81 j 

9021 

9074 

9128 

9181 

9235 

9289 

9342 

9396 

9449 

95o3 

54 

812 

9336 

9610 

9663 

9716 

977° 

9823 

9 S 77 

9930 

9984 

0037 

53 

813 

qiooqi! 

0144 

0197 

025l 

o3o4 

o358 

0411 

0464 

odi8 

057 ( 

53 

814 

0624’ 

0678 

0731 

0784 

o838 

0891 

0944 

0998 

io5i 

j 104 

53 

815 

1158 

1211 

1264 

1317 

1371 

1424 

*477 

i33o 

1584 

1637 

53 

816 

1690 

1743 

*797 

i85o 

1903 

ig56 

2009 

2o63 

2116 

2169 

53 

8*7 

2222 

2276 

2328 

2381 

2435 

2488 

254i 

2694 

2647 

2700 

53 

818 

2753 

2806 

2869 

2913 

2966 

3019 

3072 

3(25 

3178 

3231 

53 

8*9 1 

3284 

3337 

3390 I 

3443 

3496 

3549 

36o2 

3655 

3708 

3761 

53 

N. 

o j 

1 

2 

3 

4 

5 

6 

7 1 

1 

8 

9 

I). 



















































































14 A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. 

0 

1 

2 

3 

4 

1 5 

6 

7 

8 

9 

D. 

820 

913814 

3867 

3920 

3973 

4026 

4079 

4132 

4184 

4237 

4290 

53 

821 

4343 

4396 

4449 

4602 

4555 

4608 

4660 

47i3 

4766 

48x9 

53 

822 

4872 

4925 

4977 

5o3o 

5o83 

5136 

5189 

5241 

5294 

5347 

53 

823 

5400 

5453 

5oo5 

5558 

5611 

5664 

5716 

5769 

5822 

6875 

53 

824 

6927 

5 9 8 o 

6o33 

6o85 

6i38 

6191 

6243 

6296 

6349 

6401 

53 

825 

6454 

65o7 

655 9 

6612 

6664 

6717 

6770 

6822 

6875 

6927 

53 

826 

6980 

7 o 33 

7080 

7138 

7190 

7243 

7295 

7348 

7400 

7453 

53 

827 

7606 

7558 

7611 

7663 

7716 

7768 

7820 

7873 

7920 

797 8 

52 

828 

8o3o 

8o83 

8135 

8188 

8240 

8293 

8345 

8397 

845o 

8002 

52 

'829 

8555 

8607 

865 9 

871*2 

8764 

8816 

8869 

8921 

8973 

9026 

52 

83o 

QIQ078 

9i3o 

9183 

9 235 

9287 

9340 

9 3 9 2 

9444 

9496 

9649 

52 

831 

9601 

9653 

9706 

9758 

9810 

9862 

99 1 4 

9967 

®a,9 

©071 

52 

832 

920123 

0176 

0228 

0280 

o 332 

o384 

0436 

0489 

o 54 i 

o5g3 

52 

833 

0645 

0697 

0749 

0801 

o853 

0906 

o 9 58 

1010 

1062 

1114 

52 

834 

1166 

1218 

1270 

1322 

1374 

1426 

1478 

i53o 

1582 

i 634 

52 

835 

1686 

i 7 38 

1790 

1842 

1894 

1946 

1998 

2o5o 

2102 

2154 

52 

836 

2206 

2258 

23lO 

2362 

2414 

2466 

2618 

2570 

2622 

2674 

52 

837 

2725 

2777 

2829 

2881 

2933 

2085 

3 o 37 

3o8g 

3140 

3 i 9 2 

52 

838 

3244 

3296 

3348 

3399 

345 z 

35o3 

3555 

3607 

3658 

3710 

52 

83 9 

3762 

38i4 

3865 

3917 

3969 

4021 

4072 

4124 

4176 

4228 

52 

840 

924279 

4331 

4383 

4434 

4486 

4538 

4589 

4641 

4693 

4744 

52 

841 

4796 

4848 

4899 

4951 

5oo3 

5 o 54 

5106 

5157 

5200 

6261 

52 

842 

5312 

5364 

5415 

5467 

55i8 

5570 

5621 

5673 

5720 

5776 

52 

843 

5828 

5879 

5 9 3 i 

5982 

6o34 

6o85 

6137 

6188 

6240 

6291 

5x 

844 

6342 

63 9 4 

6445 

6497 

6548 

6600 

6651 

6702 

6754 

68o5 

5i 

845 

6857 

6908 

6969 

7011 

7062 

7114 

7165 

7216 

7268 

73i9 

5i 

846 

7370 

7422 

7473 

7524 

7 5 7 6 

7627 

7678 

773 o 

778 i 

7832 

5i 

847 

7883 

7935 

7986 

8 o 37 

8088 

8140 

0191 

8242 

8293 

8345 

5i 

848 

83 9 6 

8447 

8498 

8549 

8601 

8652 

8 7 o 3 

8754 

8So5 

8S5~i 

5i 

849 

8908 

8959 

9010 

9061 

9112 

9 i 63 

92 i 5 

9266 

9317 

9 368 

5i 

85o 

929419 

9470 

9 52i 

9^2 

9623 

9674 

9725 

9776 

9827 

9 8 79 

5i 

851 

9 9 3o 

9981 

©332 

®*83 

®i34 

185 

•236 

•287 

•338 

•889 

5i 

852 

930440 

0491 

o 542 

o 5 9 2 

0643 

0694 

0745 

0796 

0847 

0890 

5i 

853 

0949 

1000 

io 5 i 

1102 

1153 

1204 

1264 

i3o5 

1356 

1407 

5i 

854 

1458 

15o 9 

i56o 

l6lO 

1661 

1712 

1763 

1814 

1865 

i 9 i 5 

5i 

855 

1966 

2017 

2068 

21l8 

2169 

2220 

2271 

2322 

2372 

2423 

5i 

856 

2474 

2524 

2575 

2626 

2677 

2727 

2778 

2829 

2S79 

2 9 3 o 

5i 

85 7 

2981 

3o3i 

3o82 

3133 

3x83 

3234 

3285 

3335 

3386 

3437 

5i 

858 

3487 

3538 

358 9 

363 9 

3690 

3740 

379 1 

3841 

3892 

3943 

5i 

85 9 

3 99 3 

4044 

4094 

4145 

4195 

4246 

4296 

4347 

4397 

4448 

5 x 

860 

984498 

4549 

4599 

465 o 

4700 

475 i 

4801 

4852 

4902 

4g53 

5 o 

861 

5oo3 

5 o 54 

5 io 4 

5i 54 

52 o 5 

5255 

53 06 

5356 

5406 

5457 

5 o 

862 

5507 

5558 

56o8 

5658 

5709 

5~j5g 

5809 

586o 

5910 

5960 

5 o 

863 

6011 

6061 

6111 

6162 

6212 

6262 

6313 

6363 

6413 

6463 

5 o 

864 

65 i 4 

6564 

6614 

6665 

6715 

6765 

68x5 

6865 

6916 

6966 

5 o 

865 

7016 

7066 

7 n 7 

7167 

7217 

7267 

7817 

7 36 7 

74i8 

7468 

5 o 

866 

7518 

7568 

7618 

7668 

7718 

7769 

7819 

7869 

7919 

7969 

5 o 

867 

8019 

8069 

8119 

8169 

8219 

8269 

8320 

$370 

8420 

8470 

5 o 

868 

8520 

S5-jo 

8620 

8670 

8720 

8770 

8820 

O870 

8920 

8970 

5 o 

869 

9020 

9070 

9120 

9170 

9220 

9270 

9320 

9 36 9 

9419 

9469 

5 o 

870 

93 9 519 

9 56o 

9619 

9669 

9719 

9769 

9 8i 9 

9869 

99 l8 

9968 

5 o 

871 

940018 

0068 

0118 

0168 

0218 

0267 

0317 

o 367 

0417 

0467 

5 o 

872 

o5i6 

o566 

0616 

0666 

0716 

0765 

oSi 5 

oS65 

0918 

0964 

5 o 

8 7 3 

1014 

1064 

1 r 14 

1163 

1213 

1263 

1313 

1362 

1412 

1462 

5 o 

874 

1511 

1561 

1611 

1660 

1710 

1760 

1809 

iSSg 

I 9°9 

1968 

5 o 

8 7 5 

2008 

2 o 58 

2107 

2157 

2207 

2256 

23 o 6 

2355 

24 o 5 

2455 

5 o 

.876 

25 o 4 

2554 

26 o 3 

2653 

2702 

2762 

2801 

2851 

2901 

2 9 5 o 

5 o 

877 

3 ooo 

3 049 

3099 

3148 

3198 

3247 

3297 

3346 

33o6 

3445 

5 9 

878 

34 9 5 

3544 

35g3 

3643 

3692 

3742 

3791 

3841 

38 9 o 

3 9 3 9 

5 9 

879 

3989 

4 o 38 

4088 

4137 

4186 

4236 

4285 

4335 

4384 

4433 

79 

N. 

0 

1 

2 

_ 

3 

— 

4 

5 

6 

7 

8 

9 

D. 










































































A TABLE OF LOGARITHMS FROM 1 TO 10,000. 15 


N. 

I 

0 

I 

2 

3 

4 

5 

6 

7 

8 

9 

D.l 

8So 

044483 

4532 

458l 

4631 

4680 

4729 

4779 

4828 

4877 

4927 

49 

881 

4 9 7 6 

D023 

O074 

5i24 

5173 

5222 

6272 

5321 

5370 

5419 

49 

882 

5469 

5518 

5567 

56 i 6 

5665 

57l5 

5764 

! 58i3 

5862 

6912 

49 

883 

5961 

6010 

6o5 9 

6108 

6157 

6207 

6256 

63o5 

6354 

6403 

49 

884 

6462 

65oi 

655 i 

6600 

6649 

6698 

6747 

6796 

6845 

6894 

49 

885 

6943 

6992 

7041 

7090 

7140 

7189 

7238 

7287 

7336 

7 385 

49 

886 

7434 

7483 

7 532 

7681 

i 63 o 

7679 

7728 

7777 

7826 

7875 

49 

887 

7924 

7973 

8022 

8070 

8119 

8168 

8217 

j 8266 

8315 

8364 

49 

888 

8413 

8462 

85i 1 

856o 

8609 

8657 

8706 

8755 

8804 

8853 

49 

889 

8902 

8 9 5 i 

8999 

9048 

9097 

9146 

9 X 9 5 

9244 

9292 

9341 

49 

890 

949390 

9439 

9488 

g536 

9585 

9634 

9683 

973 i 

9780 

9829 

49 

891 

9878 

9926 

997D 

**24 

®» 7 3 

0 1 21 

®i70 

®2I9 

*267 

®3i6 

49 

892 

9 5o365 

0414 

0462 

o5i 1 

o56o 

0608 

0657 

0706 

0754 

o8o3 

49 

893 

o85i 

0900 

0949 

°997 

1046 

I0 9 5 

1143 

1192 

1240 

1289 

49 

894 

1338 

1386 

1435 

1483 

1532 

i58o 

1629 

1 677 

1726 

1775 

49 

890 

1823 

1872 

1920 

! 9 6 9 

2017 

2066 

2114 

2i63 

2211 

2260 

48 

896 

23 o 8 

2356 

24 o 5 

2453 

2502 

255 o 

2699 

2647 

2696 

2744 

48 

897 

2792 

2841 

2889 

2 9 38 

2986 

3 o 34 

3o83 

3131 

3180 

3228 

48 

898 

3276 

3325 

33 7 3 

342 i 

3470 

3518 

3566 

36i5 

3663 

3711 

48 

899 

3760 

38o8 

3856 

3 9 o 5 

3 9 53 

4001 

4049 

4098 

4146 

4 i 9 4 

48 

900 

954243 

4291 

433 9 

4387 

4435 

4484 

4532 

458o 

4628 

4677 

48 

901 

4720 

4773 

4821 

486q 

4918 

4966 

5oi4 

5 o 62 

5no 

5158 

48 

902 

6207 

5255 

53o3 

535 i 

53 9 9 

5447 

5495 

5543 

0092 

5640 

48 

9 o 3 

5688 

5736 

5784 

583 2 

588o 

5928 

5976 

6024 

6072 

6120 

48 

904 

6168 

6216 

6265 

6313 

636i 

6409 

6467 

65o5 

6553 

6601 

48 

905 

6649 

6697 

6745 

6793 

6840 

6888 

6 9 36 

6984 

7032 

7080 

48 

906 

7128 

7*76 

7224 

7272 

7320 

7868 

7416 

7464 

7512 

7009 

48 

907 

7607 

7655 

77°3 

7761 

7799 

7847 

7894 

7942 

7990 

8o38 

48 

908 

8086 

813 4 

8181 

8229 

8277 

8325 

8373 

8421 

8468 

8516 

48 

9°9 

8564 

8612 

8669 

8707 

8755 

88o3 

885o 

8898 

8946 

8994 

48 

910 

959041 

9089 

9 i3 7 

9185 

9232 

9280 

9 328 

9375 

9423 

947 1 

48 

9 H 

9 518 

9060 

9614 

9661 

97 °9 

9757 

9804 

9862 

9900 

9947 

48 

912 

999 5 

*•42 

®® 9 o 

®i38 

®i8o 

®233 

•280 

*328 

*876 

®423 

48 

9 i 3 

960471 

o5i8 

o566 

o6i3 

0661 

0709 

0756 

0804 

o85i 

0899 

48 

g»4 

0946 

0994 

1041 

1089 

1136 

1184 

I 23 1 

1279 

1326 

1374 

47 

915 

1421 

1469 

i 5 i 6 

1563 

1611 

i658 

1706 

1753 

1801 

1848 

47 

016 

1896 

1943 

1990 

2o38 

2 o 85 

2132 • 

2180 

2227 

2275 

2322 

47 

9 ! 7 

2369 

2417 

2464 

25 i 1 

2559 

2606 

2653 

2701 

2748 

W 

47 

918 

2843 

2890 

2937 

2985 

3o32 

3079 

3i26 

3i74 

3221 

3268 

47 

919 

33i6 

3363 

34io 

3457 

35 o 4 

3552 

3599 

3646 

36 9 3 

3741 

47 

920 

963788 

3835 

3882 

3929 

3 977 

4024 

4071 

4118 

4165 

4212 

47 

9 21 

4260 

4307 

4354 

44oi 

4448 

4496 

4542 

4090 

4637 

4684 

47 

922 

473 i 

477 s 

4826 

4872 

4919 

4966 

5oi3 

5o6i 

5108 

5155 

47 

923 

5202 

5249 

6296 

5343 

53 9 o 

5437 

6484 

5531 

5078 

5 62 5 

47 

924 

5672 

5719 

5766 

58i3 

586o 

5907 

5 9 54 

6001 

6048 

6o 9 5 

47 

92a 

6l42 

6189 

6236 

6283 

6329 

6376 

6423 

6470 

6517 

6564 

47 

926 

66l I 

6658 

6705 

6762 

6799 

6845 

6892 

6939 

6986 

7o33 

47 

927 

7080 

7 I2 7 

7173 

7220 

7267 

7314 

736 i 

7408 

7404 

75 oi 

47 

928 

7548 

7690 

7642 

7688 

7735 

7782 

7829 

7875 

7922 

7969 

47 

929 

8016 

8062 

8109 

8156 

8203 

8249 

8296 

8343 

83 9 o 

84.36 

47 

q 3 o 

968483 

853o 

8576 

8623 

8670 

8716 

8 7 63 

8810 

8856 

8 9 o3 

47 

9 31 

8960 

8996 

9043 

9090 

9136 

9183 

9229 

9276 

9 323 

9369 

47 

9 32 

9416 

9463 

q 5 oo 

9 556 

9602 

9649 

9695 

9742 

9789 

9835 

47 

9 33 

9882 

9928 

9975 

°°2I 

o®68 

®ii 4 

°i6i 

®207 

®254 1 

®3oo 

47 

934 

970347 

0893 

0440 

0486 

o533 

0579 

0626 

0672 

0719 

0765 

46 

q 35 

08l2 

0808 

0904 

O9OI 

°997 

1044 

1090 

1137 

1183 

1229 

46 

9 36 

1276 

1322 

1069 

1415 

1461 

i5o8 

1554 

1601 

1647 

i6o3 

46 

937 

1740 

1786 j 

1832 

1879 

1925 

1971 

2018 

2064 

2110 

2x57 

46 

9 38 

2203 

2249 j 

2296 

2342 

2388 

2484 

2481 

2627 

2573 

2619 

46 

9 3 9 

2666 

2712 j 

2708 

2804 

285 

2897 

2943 

2989 

3o35 

3o82 

46 

N. 

0 

1 

2 

3 

1 

4 

5 

6 

7 

8 

9 

D. 


25 



















































































16 A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. 

0 

j 1 

2 

3 

4 

5 

6 

7 

8 

9 

H. 

940 

973128 

0174 

3220 

3266 

33 1 3 

335 g 

34 o 5 

345 i 

3497 

3543 

46 

941 

35 go 3636 

3682 

3 7 23 

8774 

3820 

3866 

3 g 3 

8969 

4 oo 5 

46 

942 

4 o 5 t 

! 4097 

4143 

41S9 

4235 

4281 

4327 

4874 

4420 

4466 

46 

943 

45 12 

4558 

4604 

46 5 0 

4696 

4742 

4788 

4834 

4880 

4926 

46 

944 

497 2 

5 oi 8 

5 o 64 

3110 

5 1 56 

5202 

5248 

5294 

534 o 

5386 

46 

943 

5432 

5478 

5524 

5570 

56 16 

5662 

5707 

5 -j '33 

5799 

5845 

46 

946 . 

0891 

5 9 37 

5 9 83 

6029 

6075 

6121 

6 267 

6212 

6258 

6 3 04 

46 

947 

63 5 o 

6396 

6442 

6488 

6533 

6579 

6625 

I 6671 

6717 

6763 

46 

948 

6808 

6854 

6900 

6946 

6992 

7037 

7083 

7 1 29 

7173 

1 7220 

46 

949 

7266 7312 

7838 

7403 

7449 

7495 

7541 

7586 

7 632 

7678 

46 

9Do 

9777 2 4 

' 7769 

781 5 

7861 

7906 

7 9 52 

7998 

8043 

8089 

81 35 

46 

931 

8181 

8226 

8272 

83 17 

8363 

8409 

8454 

85 oo 

8546 

8591 

46 

9D2 

8637 8683 

8728 

3774 

8819 

8865 

8911 

8 9 56 

9002 

9047 

46 

953 

9093 

9138 

9184 

9230 

9273 

9321 

9366 

9412 

9437 

9-5o3 

46 

954 

9648 

9 5 94 

9639 

9685 

973 o 

9776 

9821 

9867 

9912 

9908 

46 

955 

980003; 0049 

0094 

0140 

01 85 

023 I 

0276 

0322 

0367 

0412 

45 

956 

0458 

o 5 o 3 

0549 

0594 

0640 

o 685 

oj 3 o 

0776 

0821 

0867 

45 

967 

0912 

0957 

ioo 3 

1048 

1093 

1 i 3 g 

1184 

1229 

1275 

1320 

45 

958 

1 366 

1411 

14 56 

i 5 oi 

i 547 

1592 

1637 

1683 

1728 

J 77 3 

45 

9D9 

1819 

1864 

I 9°9 

1954 

2000 

2045 

2090 

21 35 

2181 

2226 

45 

960 

982271 

i 23 16 

2362 

2407 

2452 

2497 

2543 

2588 

2633 

2678 

45 

961 

2723 

2769 

2814 

2889 

2904 

2949 

2 994 

3 o 4 o 

3 o 85 

3 1 3 o 

45 

962 

3 l 73 ( 3220 

3265 

33 10 

3356 

34 oi 

3446 

3491 

3536 

358 r 

45 

963 

3626 , 3671 

3716 

3762 

3807 

3852 

3897 

3942 

8987 

4 o 32 

45 

964 

4077 

4122 

4167 

4212 

4 267 

43 o 2 

4347 

4892 

4437 

4482 

4-5 

965 

4627 

4572 

4617 

4662 

4707 

4752 

4797 

4842 

48S7 

4932 

45 

966 

4977 

3022 

5 o 6 7 

5 11 2 

5 157 

5202 

5)2 47 

5292 

533 7 

5382 

45 

967 

5426 

5471 

55 16 

556 1 

56 o 6 

565 1 

5696 

5741 

5786 

583 o 

45 

968 

3875 6920 

5 9 65 

6010 

6 o 55 

6100 

6144 

6189 

6234 

6279 

45 

969 

6324 

6869 

641 3 

6458 

65 o 3 

6648 

65 g 3 

663 j 

6682 

6727 

45 

970 

9S6772 

6817 

6861 

6906 

6 g 5 1 

6996 

7040 

7085 

7 i 3 o 

« 7 * 7 5 

45 

97 1 

7 21 9 

7264 

7809 

7353 

7398 

7443 

7488 

7532 

7577 

7622 

45 

97 2 

7666 

7711 

7736 

7800 

7843 

7890 

7984 

7979 

8024 

8068 

45 

973 

811 3 

8 l 57 

8202 

8247 

8291 

8336 

838 1 

8425 

8470 

85 14 

45 

974 

8669 

8604 

8648 

86 g 3 

8737 

8782 

8826 

8871 

8916 

8960 

45 

973 

9006 

9049 

9094 

9 r 38 

91 83 

9227 

9 2 7 2 

93 i 6 

9361 

94 o 5 

45 

976 

q 45 o 

9494 

9589 

9 583 

9628 

9672 

9717 

9761 

9806 

9 85 o 

44 

977 

9895 

9939 

9988 

oo 2 8 

°®7 2 

8 i 17 

®i6i 

°2o6 

® 25 o 

•294 

44 

978 

99o3Jg 

o 3 b 3 

0428 

0472 

o 5 i 6 

o 56 i 

o 6 o 5 

o 65 o 

0694 

0738 

44 

979 

0783 

0827 

0871 

0916 

0960 

1004 

1049 

1093 

1137 

1182 

44 

9S0 

991226 

1270 

1 315 

1 35 q 

i 4 o 3 

1448 

1492 

1 536 

i 58 o 

1625 

44 

981 

1669 

1713 

ij 58 

1802 

1846 

1890 

1985 

1 979 

2023 

2067 

44 

982 

2111 

21 56 

2200 

2?,. j 

2288 

2333 

2377 

2421 

2465 

2509 

44 

983 

2554 

2598 

2642 

2686 j 

2730 

2 774 

2819 

2863 

2907 

2951 

44 

984 

2993 

3 o 39 

3 o 83 

3 127 

3172 

8216 

3260 

33 o 4 

3348 

33 g 2 

44 

985 

3436 

3480 

3524 

3568 j 

36 1 3 

3657 

3701 

3745 

8789 

3833 

44 

986 

3877 

3921 

8963 

4009 | 

4 o 53 

4097 

4141 

4 1 85 

4229 

4273 

44 

987 

43 i 7 

436 1 

44 o 5 

4449 I 

4498 

4537 

458 1 

4625 

4669 

47 i 3 

44 

988 

4707 

4801 

4845 

4889 

4933 

4977 

5021 

5 o 65 

5 io 8 

5 1 52 

44 

989 

5196 

6240 

5284 

5328 5372 

5416 

5460 

55 o 4 

5547 

5591 

44 

990 

9 g 5635 

0679 

6723 

5767 

58 i 1 

5854 

58 9 8 

5o42 

5 9 86 

6 o 3 o 

44 

99 1 

6074 

6117 

6161 

6206 

6249 

6293 

6337 

638 o 

6424 

6468 

4 % 

99 2 

65 12 

6555 

6899 

6643 

6687 

6781 

6774 

6818 

6862 

6906 

44 

99 J 

6949 

g 99 3 

7037 

7080 

7124 

7168 

7212 

7255 

7299 

7343 

44 

994 

7386 

743 o 

7474 

7517 

756 

j 6 o 5 

7648 

7692 

7736 

7779 

44 

993 

7823 

7867 

79m 

79^4 j 

7998 

8041 

8 o 85 

8129 

8172 

8216 

44 

996 

8259 

83 o 3 

8347 

8390 

8434 

8477 

8521 

8564 

8608 

8652 

44 

997 

86 9 5 

8789 

8782 

8826 

8869 

8 gi 3 

8 g 56 

9000 

9043 

9087 

44 

998 

91 3 1 

9174 

9218 

9261 

93o5 

9348 

9892 

9435 

9479 

9522 

44 

999 

9565 

9609 

9652 

9696 

9739 

9783 

9826 

9870 

99 l3 

99 5 7 

43 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 




















































































A TABLE 


OF 

LOGARITHMIC 

SINES AND TANGENTS 

FOR EVERY 

DEGREE AND MINUTE 
OF THE QUADRANT. 


Remark. The minutes in the left-hand column of each 
page, increasing downwards, belong to the degrees at the 
top; and those increasing upwards, in the right-hand column, 
belong to the degrees below. 



18 


(0 DEGREES.) A TABLE OF LOGARITHMIC 


M. 


9 

10 

11 

12 

1 3 

14 

1 5 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 
2 

2 

3? 

3 1 

32 

33 

34 

35 

36 
3 
3 

39 

40 

4 1 

42 

43 

44 

45 

46 

47 

48 
P 

5 0 

5 1 

52 

53 

54 

55 

56 

5 ? 

58 

5 9 

60 


Sine 


6- 463726 
764766 
940847 

7- 065786 
162696 
241877 
308824 
3668 i 6 
417968 
463725 

7 * 5 o 5 ii 8 

542906 

577668 

609853 

639816 

667845 

694173 

718997 

742477 

764754 

7-785943 

806146 

825461 

843934 

861662 
878695 
895085 
910879 
926119 
940842 

7- 955082 

968870 

982263 

995198 

8- 007787 
020021 
031919 
043601 
064781 
066776 

8-076500 

086965 

097183 

107167 

116926 

126471 

i 358 io 

144953 

153907 

162681 

8-171280 
179713 
187985 
196102 
204070 
2 ii 8 o 5 
219581 
227134 
234557 
241856 


D. 


Cosine 


5017-17 
2934-86 
2082*31 
161 5 •17 
1 3 19•68 
1116-75 
066-53 
852-54 
762-63 

689-88 

629-81 

579-36 

536 - 4 i 

499-38 

467-14 

438 •81 
4 i 3 • 72 
391-35 
371-27 
353 -i 5 

336-72 
32 i-75 
3 o 8 -o 5 

295.47 

283-88 

273-17 

263-26 

253-99 

245-38 

237-33 

229-80 
222-73 
216-08 
209-81 
206-90 
198-31 
193-02 
188-01 
1S 3•25 
178-72 

174-41 
I 7 o- 3 i 
i 66 - 3 o 
162-66 
159-08 
i 55-66 
1 52-38 
149-24 
146-22 
143-33 

i 4 o -54 
137 •86 
136-29 
i 32 - 8 o 
i 3 o- 4 i 
128-10 
125-87 
123-72 
121-64 
119-63 


D. 


Cosine 


10-000000 

000000 

000000 

000000 

000000 

000000 

9.999999 

999999 

999999 

999999 

999998 

9-999998 

999997 

999997 

999996 

999996 

999995 

999995 

999994 

999993 

999993 

9.999992 

999991 

999990 

999989 

999988 

999988 

999987 

999986 

999985 

999983 

9-999982 

999981 

999980 

999979 

999977 

999976 

999975 

999973 

999972 

999971 

9.999969 

999968 

999966 

999964 

Q99963 

999961 

999959 

999958 

999956 

999954 

9-999952 

999950 

999948 

999946 

999944 

999942 

999940 

999938 

999936 

999934 


D. 


Sine 


• 00 

• 00 

• 00 
-00 

• 00 

• 01 
•01 
•01 
•01 
•01 

-oi 

• 01 

• 01 
-oi 

• 01 

• 01 

• 01 

• 01 

• 01 

• 01 

•01 

•01 

•01 

•02 

•02 

•02 

• 02 

• 02 
•02 

• 02 

■02 

■02 

■02 

•02 

•02 

•02 

•02 

•02 

■02 

• 02 

•02 

• 02 
-02 
■o 3 
■o 3 
•o 3 
>o 3 
•o 3 
•o 3 
•o 3 

•o 3 

■o 3 

■o 3 

•o 3 

•o 3 

•04 

• 04 
•04 

• 04 

• 04 


Tang. 


0-000000 

6- 463726 
764756 
940847 

7- 065786 
162696 
241878 
308825 
366817 

417970 

463727 

7 *5o5i2o 

542909 

577672 

609867 

639820 

667849 

694179 

719004 

742484 

764761 

7-785951 

8 o 6 i 55 

825460 

843944 

861674 

878708 

896099 

910894 

926134 

94 o 858 

7 - 955 ioo 
968889 

982253 

995219 

8- 007809 
020046 
031945 
043627 
054809 
066806 

8-076531 

086997 

097217 

107202 

116963 

126610 

i 3585 i 

i 44 qq 6 

153962 

162727 

8-171328 
179763 • 
i 8 oo 36 
196156 
204126 
211953 
219641 
227195 
234621 
241921 


D. 


Cotang. 


5017-17 
2934-83 
2082 - 3 l 
161 5 •17 
i 3 i 9 - 6 o 
iii 5 - 7 o 
096-53 
062-54 
762-63 

689-88 

629-81 

579-33 

536-42 

499-39 
467•16 
438-82 
4 i 3-73 
391 -36 
371-28 
35 i -36 

336-73 

3121-76 

3 o 8 -o 6 

2 q 5-49 

283-90 

273-18 

263-25 

254 -oi 

246-40 

237-35 

229-81 
222-75 
216-10 
209-83 
206-92 
198-33 
io 3 -o 5 
108•o 3 
183*27 
I 78-74 

174-44 
i-jo-34 
166-42 
162-68 
159-10 
1 55•68 
i 52 - 4 i 
149-27 
146-27 
143-36 

140-57 
137-90 
i 35-32 
i 32-84 
i 3 o -44 
128-14 
125-90 
123-76 
121-68 
119-67 


Cotang. 


D. 


Infinite. 
i3-536274 
235244 
059153 
12-934214 
837304 
756122 
691175 
633 1 83 
582 o 3 o 
536273 

12-494880 
467091 
422328 
390143 
36 oi 8 o 
332 1 5 i 
3o582i 
280997 
257616 
236239 

12-214049 
193846 
174540 
i 66 o 56 
138326 
121292 
104901 
089106 
078866 
069142 

12 - 044900 
o 3 1111 

017747 

004781 
-992191 
970965 
968055 
956473 
945191 
934194 

■923469 
9i3oo3 
902783 
802797 

883087 
873490 
864149 
856004 
846048 
837273 

11-828672 
820287 
811964 
803644 
796874 
788047 
780369 
772806 
765379 
758079 


11 


11 


Tang. 


60 

69 

58 

5 ? 

56 

55 

54 

53 

62 

5 i 

5 o 

49 

48 

47 

46 

45 

44 

43 

42 

4 i 

4 o 

3 9 

38 

37 

36 

35 

34 

33 

32 

3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

10 
l8 

n 

16 

16 

14 

i 3 

12 

11 
10 


7 

6 

5 

4 

3 

2 

1 

o 


M„ 


(89 DEGREES.) 


































SINES AND TANGENTS. (1 DEGREE.) 


19 


M. 

Sine 

0 

8 • 241 855 

1 

249033 

2 

256094 

3 

263042 

4 

269881 

5 

276614 

6 

283243 

7 

289773 

8 

296207 

9 

302546 

10 

308794 

11 

8 - 3 i 49 o 4 

12 

321027 

i 3 

327016 

14 

332924 

i 5 

338753 

16 

3445 o 4 

17 

35 oi 8 i 

18 

355783 

J 9 

36 1 3 1 5 

20 

366777 

21 

8-372171 

22 

377499 

23 

382762 

24 

387962 

25 

393101 

26 

398179 

27 

403199 

28 

408161 

29 

4 i 3 o 68 

3 o 

417919 

3 i 

8-422717 

32 

427462 

33 

432 1 56 

34 

4368 oo 

35 

441394 

36 

445941 

37 

45 o 44 o 

38 

454893 

3 9 

459301 

4 o 

463665 

4 i 

8-467983 

42 

472263 

43 

44 

476498 

480693 

45 

484848 

46 

488963 

47 

493040 

48 

497078 

49 

5 oio 8 o 

5 o 

5 o 5 o 45 

5 1 

52 

8-608074 
512067 

53 

516726 

54 

52 o 55 i 

55 

524343 

56 

528102 

57 

53 i 828 

58 

535523 

5 9 

539186 

60 

542819 

1 

Cosine 


16 


D. 

Cosine 

D. 

Tang. 

D. 

119-63 

117-68 

11 5 -80 
113*98 
112-21 
iio- 5 o 
io 8-83 
107-21 
io 5-65 

104•1 3 
102-66 

101•22 
99 • 82 

98-47 

97-14 

93- 86 

94- 60 
93-38 

9 2- I 9 

91 -o 3 
89.90 

88-80 
87.72 
86-67 
85-64 
84-64 

83-66 
82-71 
81 *77 
80 -86 
79-96 

79-°9 
78-23 

77 - 4 o 

76-67 

75.77 

74-99 

74-22 

73-46 

72-73 

72-00 

71-29 
70-60 
69-91 
69-24 
68-59 
67.94 
67 - 3 1 
66-6q 
66-08 
65-48 

64-89 
64 - 3 1 
63-75 
63 • 19 
62-64 

62-11 

61 -58 
61 -06 
60 -55 
60-04 

9.999934 

999932 

999929 

999927 

999925 

999922 

999920 

999918 

999915 

9999 13 
999910 

9-999907 

99 99 o 5 

999902 

999899 

999897 

999894 

999891 

999888 

999886 

999882 

9.999879 

999876 

999873 

999870 

999867 

999864 

999861 

999858 

999854 

999851 

9-999848 

999844 

999841 

999838 

999834 

999831 

999827 

999823 

999820 

999816 

9-999812 

999809 

999800 

999801 

999797 

999793 

9997 ?o 

999786 

999782 

999778 

9-999774 

999769 

999765 

999761 

999707 

999753 

999748 

999744 

999740 

9997 3:} 

•04 

• 04 
•04 
•04 

• 04 
•04 

• 04 

• 04 

• 04 

• 04 
-04 

• 04 

• 04 

• 04 

• o 5 

• o 5 

• o 5 

• o 5 

• o 5 

• o 5 

• o 5 

•o 5 

• o 5 

• o 5 

• o 5 
-o 5 

• o 5 

• o 5 
-o 5 

• o 5 

• 06 

• 06 

• 06 

• 06 

• 06 

• 06 

• 06 

• 06 
•06 
-06 
•06 

• 06 

• 06 

• 06 

• 06 

•07 

-07 

•07 

•07 

•07 

•07 

•07 

•07 

•07 

-07 

•07 
•07 | 

•07 

•07 

•07 

•07 

8-241921 
249102 
25 oi 65 
263 i1 5 
269956 
276691 
283323 
289856 
296292 
3 o 2634 
3 o 8884 

8• 3 15046 
321122 
327114 
333025 
338856 
344610 
350289 
355896 

36 i 43 o 

3668 9 5 

8-372292 
377622 
382889 
388092 
3 9 3234 
3983 i 5 
4 o 3338 
4 o 83 o 4 
41321 3 

418068 

8-422869 
427618 
4323 1 5 
436962 

44 i 56 o 

446110 

45 o 6 i 3 

455070 

459481 

463849 

8-468172 

472454 

476693 

480892 

485 o 5 o 

489170 

4 9 325 o 

497293 

601298 

* 5 o 5267 

8-609200 

513098 

516961 

620790 

524586 

628349 

532 o 8 o 

535779 
53 9 447 
543084 

119-67 

H 7-72 

11 5 •84 
114-02 
112-25 
iio -54 
108-87 
107-26 
105-70 
104•18 
102-70 

101•26 
99.87 
98-61 

97 " J 9 
95-90 

94-65 
9 3 -43 
92 • 24 

01 - 08 

89 - 9 5 

88-85 

87.77 

86.72 

85-70 
84-70 
83 71 
82-76 
81 -82 
80-91 
80-02 

79-14 

78 - 3 o 

77-45 

76-63 

75-83 

75 -o 5 

74-28 

73-52 

72-79 

72-06 

71-35 
70-66 
69-98 
69 • 3 1 
68-65 
68-oi 
67.38 
66-76 
66 -1 5 
65-55 

64-96 
64-39 
63-82 
63-26 
62-72 
62-18 
61 -65 
61 -1 3 
60-62 
60 • 12 

D. 

Sine 


1 

Cotang, j D. 


(88 DEGREES.) 


Cotang. 


i1-758079 
750898 
743835 
736885 
730044 
723309 
716677 

710144 
703708 
.697366 
691116 


S 8 
6 

666975 
661144 
655390 

649711 

644 io 5 

638570 

633 io 5 


60 

I 

5 7 

56 

55 

54 

53 

52 

5 i 

5 o 

49 

48 

% 

45 

44 

43 

42 

4 i 

40 


11-627708 
622378 
617111 
611908 
606766 
6 oi 685 
596662 
691696 
586787 
581932 


3 9 

38 

3 ? 


36 

35 


34 

33 

32 

3 i 

3 o 


11•5771 3 1 

672382 
56 7 685 
563 o 38 
558440 
553890 
549387 
544 q 3 o 
540D19 
536 1 5 1 


29 

28 

27 

26 

25 

24 

23 

22 

21 

20 


II- 53 l 828 
527546 
523307 
519108 
Sl^So 
5 io 83 o 
506750 
502707 
498702 

494733 


19 

18 

17 

16 
i 5 
1 4 
i 3 
12 
11 
10 


11•490800 
406902 
483 o 39 
479210 
476414 
471 65 1 
467920 
464221 
46 o 553 
456916 


7 

6 

5 

4 

3 


2 

1 

o 


Tang 

















































20 ' (2 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

8*542819 

60*04 

9*999735 

*07 

8 * 543 o 84 

60 • 12 

11*456916 

60 

i 

546422 

5 9 *55 

999731 

*07 

54669 1 

59*62 

453309 

5 o 

2 

649995 

59*06 

999726 

.07 

550268 

69* 14 

449732 

58 

3 

553539 

58*58 

999722 

• 08 

553817 

58*66 

446 i 83 

57 

4 

557054 

58 *ii 

999717 

*08 

55 7 336 

58*19 

442664 

56 

5 

56 o 54 o 

57*65 

999713 

.08 

560828 

57.73 

439172 

55 

6 

563999 

57*19 

999708 

.08 

664291 

57*27 

435709 

54 

n 

56743 i 

56*74 

999704 

•08 

567727 

* 56*82 

432273 

53 

8 

570836 

56 * 3 o 

999699 

•08 

571137 

56*38 

428863 

52 

9 

674214 

55.87 

999604 

•08 

5*74520 

55*95 

425480 

5 i 

IO 

577566 

55 *44 

999689 

• 08 

577877 

55*52 

422123 

5 o 

11 

8*580892 

55*02 

9*999685 

.08 

8 * 58 i 2 o 8 

55 *io 

11*418792 

49 

12 

584193 

54 * 6 o 

999680 

.08 

5845 1 4 

54*68 

4 i 5486 

48 

i 3 

587469 

54 -19 

999675 

.08 

587795 

54*27 

4 l 2205 

47 

14 

59072i 

53*79 

999670 

.08 

591001 

53*87 

408949 

46 

i 5 

593948 

53 * 3 9 

999665 

• 08 

594283 

53*47 

406717 

45 

16 

597152 

53 *oo 

999660 

• 08 

597492 

53 * 08 

4 o 25 o 8 

44 

l l 

6 oo 332 

52 • 61 

999655 

.08 

600677 

52*70 

899328 

43 

18 

603489 

52*23 

999650 

.08 

6 o 383 9 

52*32 

396161 

42 

19 

606623 

5 i -86 

999645 

.09 

606978 

5 i *94 

398022 

4 i 

20 

609734 

5 i 49 

999640 

•°9 

610094 

5 i *58 

389906 

40. 

21 

8*612823 

5 1 • 12 

9*999635 

*09 

8•61 3 189 

5 1 • 21 

11• 3868 11 

39 

22 

615891 

60*76 

999629 

• 09 

616262 

5 o *85 

383738 

38 

23 

618987 

5 o* 4 i 

999624 

•09 

6.1931 3 

5 o* 5 o 

380687 

87 

24 

621962 

5 o*o 6 

999619 

*09 

622343 

5 o* 1 5 

377657 

36 

25 

624965 

49*72 

999614 

• 09 

625352 

49*81 

374648 

35 ' 

26 

627948 

49*38 

999608 

.09 

628340 

49-47 

371660 

34 

27 

630911 

49*04 

999603 

*09 

63 i 3 o 8 

49* i 3 

368692 

33 

28 

633854 

48*71 

999597 

• 09 

634256 

48 • 80 

365744 

32 

29 

636776 

48*39 

999592 

• 09 

637184 

48*48 

362816 

3 i 

3 o 

639680 

48*06 

999586 

•°9 

640093 

48* 16 

359907 

3 o 

3 1 

8*642563 

47 * 7 5 

9*999681 

.09 

8*642982 

47-84 

11 *357018 

29 

32 

645428 

47*43 

99 9 5 7 5 

•°9 

645853 

47-53 

354147 

28 

33 

648274 

47*12 

999570 

• 09 

648704 

47-22 

351296 

27 

34 

65 1102 

46*82 

999564 

.09 

65 1537 

46*91 

348463 

26 

35 

653911 

46*52 

999558 

• I 0 

654352 

46*61 

846648 

25 

36 

656702 

46*22 

999553 

• 10 

657149 

46 * 3 i 

34285 i 

24 

37 

659475 

45*92 

999647 

• 10 

659928 

46*02 

340072 

23 

38 

66223o 

45*63 

999641 

• 10 

662689 

45*73 

3373 i1 

22 

3 g 

664968 

45*35 

999535 

• 10 

665433 

45*44 

334567 

21 

40 

667689 

45 *o 6 

999629 

• 10 

668160 

45*26 

33 i 84 o 

20 

4 i 

8*670393 

44*79 

9*999524 

• 10 

8*670870 

44*88 

11*329130 

*9 

42 

678080 

44 * 5 i 

999518 

• 10 

673563 

44 * 6 i 

326437 

18 

43 

676751 

44*24 

999512 

• 10 

676239 

44-34 

323761 

17 

44 

678405 

43*97 

999506 

• 10 

678900 

44-17 

321 100 

10 

45 

68 io 43 

43.70 

999500 

• 10 

68 i 544 

43 • 80 

3 1 8456 

i 5 

46 

683665 

43 * 44 

999493 

• 10 

684172 

43*54 

3 i 5828 

14 

47 

686272 

43 * 18 

999487 

• 10 

686784 

43*28 

3 1 32 j 6 

i 3 

48 

688863 

42*92 

999481 

• 10 

689381 

43 *o 3 

310619 

12 

49 

691438 

42*67 

999473 

• 10 

691963 

42*77 

3 o 8 o 37 

11 

5 o 

693998 

42*42 

999469 

• 10 

694529 

42*52 

3 o 547 i 

10 

5 i 

8*696543 

42*17 

9*999463 

• 11 

8*697081 

42*28 

11*302919 

0 

52 

699073 

41 *92 

999456 

• 11 

699617 

42 *o 3 

3 oo 383 

8 

53 

701589 

41 *68 

999460 

• 11 

702139 

* 4 i *79 

297861 

7 

54 

704090 

4 1 • 44 

999443 

• 11 

704646 

41 -55 

295354 

6 

55 

706577 

41*21 

999437 

• 11 

707140 

41 -32 

292860 

5 

56 

709049 

40*97 

99943 i 

• 11 

709618 

41 *08 

200382 

4 

57 

711607 

40*74 

999424 

• 11 

712083 

4 o *85 

287917 

3 

58 

713952 

4 o* 5 i 

999418 

• 11 

714534 

40*62 

286466 

2 

5 9 

716383 

40*29 

999411 

• 11 

716972 

40*40 

283028 

1 

60 

718800 

4o*o6 

999404 

• 11 

719396 

40*17 

280604 

0 


Cosine 

D. 

Sine 


Cotang. 

D. 

Tang. 

M, 


(87 DEGREES.) 
















































SINES AND TANGENTS. (3 DEGREES.) 


21 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

8-718800 

4o-o6 

9-999404 

• 11 

8-719396 

40-17 

11•280604 

60 

i 

721204 

89-84 

999398 

• 11 

721806 

39-96 

278.94 

59 

2 

723595 

39-62 

999391 

• 11 

724204 

39-74 

276796 

58 

57 

3 

725972 

39-41 

999384 

• 11 

726588 

39-52 

273412 

4 

728337 

39-19 

999378 

• 11 

728959 

39- 3 o 

271041 

56 

5 

730688 

38 .98 

99937. 

• 11 

73 1 3 17 

39-09 

268683 

55 

6 

733027 

38-77 

999364 

• 12 

733663 

38-89 

266337 

5.4 

7 

735354 

38-57 

999357 

• 12 

735996 

38-68 

264004 

53 

8 

737667 

38-36 

999350 

• 12 

7383 17 

38-48 

261683 

52 

9 

739969 

38 -16 

999343 

•. 2 

740626 

38-27 

• 259374 

5 i 

IO 

742259 

37-96 

999336 

• 12 

742922 

38-07 

267078 

5 o 

11 

8-744536 

37-76 

9-999329 

• 12 

8-746207 

37-87 

11-254793 

49 

12 

746802 

37*56 

999322 

• 12 

747479 

37-68 

252521 

48 

i 3 

749055 

37-37 

99931 5 

• 12 

749740 

37-49 

250260 

47 

i 4 

751297 

37-17 

999308 

• 12 

76.989 

37-29 

248o.I 

46 

i 5 

753528 

36-98 

99 g 3 oi 

-12 

764227 

37 • 10 

245773 

45 

16 

755747 

36-79 

999294 

• 12 

756453 

86-92 

243547 

44 

17 

757955 

36 - 6 . 

999286 

• 12 

758668 

36-73 

241332 

43 

18 

76 oi 5 i 

36-42 

999279 

• 12 

760872 

36-55 

239128 

42 

*9 

762337 

36-24 

999272 

• 12 

763 o 65 

36-36 

236935 

4 i 

20 

7645 i1 

36 -06 

999265 

• 12 

765246 

36 -18 

234754 

40 

21 

8-766675 

35-88 

9.999257 

• 12 

8-7674.7 

36 -oo 

1 1-232583 

39 

22 

768828 

35-70 

999260 

• i 3 

769578 

35-83 

230422 

38 

23 

770970 

35-53 

999242 

• i 3 

771727 

35-65 

228273 

37 

24 

773 ioi 

35-35 

999235 

• i 3 

773866 

35-48 

226134 

36 

25 

775223 

35 -i 8 

999227 

• i 3 

775995 

35 - 3 i 

224 oo 5 

35 

26 

777333 

35 -oi 

999220 

• i 3 

778114 

35 -i 4 

221886 

34 

27 

779434 

34-84 

999212 

• i 3 

780222 

34-97 

219778 

33 

28 

78024 

34-67 

999205 

• i 3 

782820 

34 - 8 o 

217680 

32 

29 

7836 o 5 

34 - 5 i 

999197 

• i 3 

784408 

34-64 

215592 

3 i 

3 o 

786675 

34 ■ 3 1 

999189 

• i 3 

786486 

34-47 

21 3 5 14 

3 o 

3 i 

8-787736 

34 -18 

9-999181 

• i 3 

8-788554 

34 - 3 1 

11-211446 

29 

32 

789787 

34-02 

999174 

• i 3 

7906.3 

34-15 

209887 

28 

33 

791828 

33-86 

999166 

• i 3 

792662 

33-99 

207338 

27 

34 

793869 

33-70 

999 .58 

• i 3 

794701 

33-83 

206299 

26 

35 

796881 

33-54 

999.50 

• i 3 

796731 

33-68 

203269 

25 

36 

797894 

33-39 

999142 

• i 3 

798762 

33-52 

201248 

24 

37 

799897 

33-23 

999 r 34 

• i 3 

800763 

33-37 

199237 

23 

38 

80.892 

33 -o 8 

999126 

• i 3 

802765 

33-22 

197235 

22 

3 9 

803876 

32-93 

999118 

• i 3 

804758 

33-07 

196242 

21 

40 

8 o 5852 

32-78 

999110 

• i 3 

806742 

32-92 

193268 

20 

41 

8-807819 

32-63 

9-999102 

• i 3 

8-808717 

32-78 

II•191283 

19 

42 

809777 

32-49 

999094 

• 14 

81o 683 

32-62 

189817 

l8 

43 

811726 

32-34 

999086 

•14 

812641 

32-48 

187309 

17 

44 

8 . 366 -. 

32 - 19 

999077 

• 14 

814589 

32-33 

186411 

l6 

45 

816699 

32 -o 5 

999069 

• 14 

8.6629 

32-19 

183471 

i 5 

46 

817622 

3 i -91 

99906. 

• 14 

818461 

32 -o 5 

18.539 

i 4 

47 

819436 

3 1 - 77 

999053 

•14 

820384 

31-91 

179616 

i 3 

43 

82 i 343 

3 1 -63 

999044 

• 14 

822298 

3 . -77 

177702 

12 

49 

823240 

3 1 - 49 

999036 

•14 

824205 

3 1 - 63 

176795 

11 

5 o 

825 i 3 o 

3 1 • 35 

999027 

• i 4 - 

826103 

3 . - 5 o 

178897 

10 

5 i 

8-827011 

3 . -22 

9 - 999^9 

.14 

8-827992 

3 1 * 36 

11 • 172008 

2 

52 

828884 

3 i - 08 

999010 

•14 

829S74 

3 1 - 23 

170126 

8 

53 

830749 

3 o-g 5 

999002 

•14 

83.748 

3 i-10 

.68252 

7 

54 

832607 

3 o -82 

998993 

•14 

8336.3 

30-96 

1 66387 

6 

55 

834456 

3 o- 6 g 

998984 

•14 

835471 

3 o -83 

164529 

5 

56 

836297 

3 o -56 

998976 

• i 4 

837321 

3o-70 

162679 

4 

57 

58 

838 1 3 o 
839956 

3 o -43 

3 o- 3 o 

998961 

998968 

• i 5 

• i 5 

839.63 

840998 

30-67 

3 o -45 

160837 

169002 

3 

2 

5 9 

841774 

3 o-17 

998960 

• i 5 

842825 

3 o -32 

157.76 

1 

60 

843585 

3 o-oo 

99S941 

• i 5 

844644 

3 °-19 

1 55356 

0 


Cosine 

D. 

Sine 


Cotang. 

D. 

Tang. 

M. 


(86 DEGREES.) 

















































22 (4 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

8-843585 

3 o-o 5 

9-998941 

• i 5 

8-844644 

3 o-19 

11 • 1 55356 

60 

i 

845387 

29-02 

998932 

• i 5 

846455 

30-07 

i 53545 

5 q 

2 

847183 

29-80 

998923 

• i 5 

848260 

29-96 

151740 

58 

3 

848971 

29-67 

998914 

• i 5 

860067 

29-82 

1 49943 

57 

4 

850761 

29-55 

998905 

■ i 5 

85 1846 

29-70 

148164 

56 

5 

852525 

29 • 43 

998896 

• i 5 

853628 

29-58 

146372 

55 

6 

854291 

29 • 3 1 

998887 

• i 5 

8554 o 3 

29-46 

144597 

54 

7 

856049 

29-19 

998878 

• i 5 

857171 

29-35 

142829 

53 

8 

867801 

29-07 

998869 

• i 5 

858932 

29-23 

141068 

52 

9 

85 9 546 

28-96 

998860 

• i 5 

860686 

29-11 

139314 

5 i 

10 

861283 

28-84 

998851 

• i 5 

862433 

29-00 

137567 

5 o 

11 

8 - 863 oi 4 

28-73 

9-998841 

• i 5 

8-864173 

28-88 

11•135827 

49 

12 

864738 

28-61 

998832 

• i 5 

865906 

28-77 

134094 

48 

i 3 

866455 

28- 5 o 

998828 

• 16 

867632 

28-66 

132368 

47 

14 

8681 65 

28-39 

998813 

• 16 

869351 

28-54 

130649 

46 

i 5 

869868 

28-28 

998804 

• 16 

871064 

28-43 

128936 

45 

16 

871565 

28-17 

998795 

• 16 

872770 

28-32 

127230 

44 

17 

8 7 3255 

28-06 

998785 

• 16 

874469 

28-21 

1 2553 i 

43 

18 

874938 

27-96 

998776 

• 16 

876162 

28-11 

123838 

42 

19 

876615 

27-86 

998766 

• 16 

877849 

28-00 

12 21 5 1 

4 i 

20 

878285 

27-73 

998757 

• 16 

879529 

27-89 

120471 

4 o 

21 

8-879949 

27-63 

9-998747 

• 16 

8-881202 

27-79 

11•118798 

39 

22 

881607 

27-62 

998738 

• 16 

882869 

27-68 

1171 3 1 

38 

23 

883258 

27-42 

998728 

• 16 

88453 o 

27-68 

116470 

37 

24 

884903 

27 • 3 1 

998718 

•16 

8861 85 

27-47 

11 38 1 5 

36 

25 

886042 

27-21 

998708 

• 16 

887833 

27-37 

112167 

35 

26 

888174 

27-11 

998699 

• 16 

889476 

27-27 

1io 524 

34 

27 

889801 

27-00 

998689 

• 16 

891112 

27-17 

108888 

33 

28 

891421 

26-90 

998679 

• 16 

892742 

27-07 

107258 

32 

29 

893035 

26-80 

998669 

•n 

894366 

26-97 

io 5634 

3 i 

3 o 

894643 

26-70 

998669 

•17 

896984 

26-87 

104016 

3 o 

3 i 

8-896246 

26-60 

9-998649 

•n 

8-897596 

26-77 

11•102404 

29 

32 

897842 

26 - 5 i 

998639 

•17 

899203 

26-67 

100797 

28 

33 

899432 

26-41 

998629 

•17 

900803 

26-58 

° 99 I 97 

27 

34 

901017 

26 - 3 i 

998619 

•17 

902398 

26-48 

097602 

26 

35 

902596 

26-22 

998609 

•H 

903987 

26-38 

096013 

25 

36 

904169 

26-12 

998599 

•n 

905070 

26-29 

094430 

24 

37 

906736 

26-o 3 

998689 

■ 17 

907147 

26-20 

092853 

23 

38 

907297 

25-93 

99 85 7 8 

• ! 7 

908719 

26-10 

091281 

22 

3 9 

908853 

25-84 

998668 

•17 

910285 

26-01 

089716 

21 

4 o 

910404 

25-76 

998558 

-17 

911846 

25-92* 

088154 

20 

41 

8-911949 

25-66 

9-998548 

•17 

8-913401 

25-83 

11-086599 

IO 

42 

913488 

25-56 

998537 

• 17 

914951 

25-74 

085049 

l 8 

43 

9l5o22 

25-47 

998527 

•17 

916495 

25-65 

o 835 o 5 

17 

44 

9 i 655 o 

25-38 

998616 

•18 

918034 

25-56 

081966 

10 

45 

918073 

25-29 

998506 

•18 

919568 

25-47 

080432 

i 5 

46 

919591 

25-20 

998495 

•18 

921096 

25-38 

078904 

14 

47 

921103 

25-12 

998485 

•18 

922619 

25 - 3 o 

077481 

i 3 

48 

922610 

25 -o 3 

998474 

•18 

924136 

25-21 

076864 

12 

49 

924112 

24-04 

998464 

•18 

925649 

25-12 

074351 

11 

5 o 

925609 

24-86 

998453 

•jS 

927166 

25 -o 3 

072844 

10 

5 i 

8-927100 

24-77 

9-998442 

• 18 

8-928658 

24 -q 5 

11-071342 

9 

52 

928587 

24-69 

998431 

• 18 

9001 55 

24-86 

069845 

8 

53 

930068 

24-60 

998421 

• 18 

931647 

24-78 

068353 

7 

64 

931 544 

24-52 

998410 

•18 

933 i 34 

24-70 

066866 

6 

55 

933 oi 5 

24-43 

998399 

-18 

934616 

24-61 

o 65384 

5 

56 

934481 

24-35 

998388 

• 18 

936093 

24-53 

063907 

4 

rl 

935942 

24-27 

998377 

• 18 

937665 

24-45 

062435 

3 

58 

937698 

24-19 

998866 

•18 

939032 

24-37 

060968 

2 

i 9 

93885 o 

24-11 

998355 

• 18 

940494 

24 - 3 o 

059606 

1 

60 

940296 

24-o 3 

998344 

• 18 

941902 

24-21 

058048 

0 

I Cosine 

D. 

Sine 


Cotang. 

D. 1 

Tang. 

M. 


(85 DEGREES.) 







































SINES AND TANGENTS. (5 DEGREE.) 


23 


D. 

Tang. 

D. 

Cotang. 


• i 9 

8-941952 

24-21 

11•058048 

60 

• 19 

943404 

24* i 3 

056696 

5 9 

-i 9 

944852 

24-o 5 

o 55 i 48 

58 

• 1 9 

946295 

23-97 

053706 

5 7 

-19 

947734 

23-00 

o 52266 

56 

• 19 

949168 

23-82 

o 5 o 832 

55 

• 19 

9O0O97 

23-74 

049403 

54 

•19 

952021 

23-66 

047979 

53 

.19 

953441 

23 -6o 

046609 

52 

• 19 

964866 

23 • 5 1 

046144 

5 i 

• 19 

966267 

23-44 

043733 

5 o 

• 19 

8-957674 

23-37 

11-042326 

49 

.19 

969076 

23-29 

040925 

48 

.19 

960473 

23-23 

039027 

47 

•19 

961866 

23-14 

o 38 i 34 

46 

.19 

963255 

23-07 

036745 

45 

.19 

964639 

23-00 

o 3536 i 

44 

.19 

966019 

22 -o 3 

033981 

43 

• 20 

967394 

22-86 

032606 

42 

• 20 

968766 

22-79 

o 3 i 234 

4 i 

• 20 

970133 

22-71 

029867 

40 

• 20 

8-971496 

22-65 

11-o 285 o 4 

39 

• 20 

972805 

22-67 

027145 

38 

• 20 

974209 

22 • 5 l 

026791 

37 

• 20 

97556 o 

22-44 

024440 

36 

• 3 P 

976906 

22-37 

023094 

35 

• 20 

978248 

22 • 3 o 

021702 

34 

• 20 

979586 

22-23 

020414 

33 

• 20 

980921 

22-17 

019079 

32 

• 20 

982261 

22-10 

017749 

3 i 

• 20 

983577 

22-04 

016423 

3 o 

• 20 

8•984899 

21 '97 

11-oiSioi 

29 

• 20 

986217 

21 -91 

013783 

28 

• 20 

987532 

21-84 

012468 

27 

• 20 

988842 

21-78 

0111 58 

26 

• 21 

990149 

21-71 

009861 

25 

• 21 

991451 

21 -65 

008549 

24 

• 21 

992760 

2 i -58 

007260 

23 

• 21 

994045 

21-52 

006955 

22 

• 21 

995337 

21-46 

004663 

21 

• 21 

996624 

21-40 

003376 

20 

• 21 

8-997908 

21-34 

11-002092 

19 

• 21 

99Q188 

21-27 

000812 

l 8 

• 21 

9•ooo465 

21-21 

10-999535 

n 

• 21 

001738 

2 I - 15 

998262 

10 

• 21 

oo3oo7 

21-09 

996993 

i 5 

• 21 

004272 

21 -o 3 

995728 

i 4 

• 21 

oo 5534 

20-97 

994466 

i 3 

• 21 

006792 

20-01 

993208 

12 

• 21 

008047 

20-85 

991953 

11 

• 21 

009298 

20-80 

990702 

10 

• 21 

9-010646 

20-74 

10-989454 

9 

• 21 

011790 

20-68 

988210 

8 

• 21 

oi 3 o 3 i 

20-62 

986969 

7 

• 22 

014268 

20-56 

985732 

6 

• 22 

oi55o2 

20-5i 

984498 

5 

• 22 

016732 

20-45 

983268 

4 

• 22 

017959 

20-40 

982041 

3 

• 22 

019183 

20-33 

980817 

2 

• 22 

020403 

20-28 

979597 

1 

• 22 

021620 

20-23 

978380 

0 


Cotang. 

D. 

Tang. 

M. 


M. 


o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

1 3 

14 

1 5 

16 

l l 

i8 

20 

21 
22 

23 

24 

25 

26 

2 7 

28 

3 0 

3 1 

32 

33 

34 

35 

36 
3 
3 

3 9 

4 0 

4 1 

42 

43 

44 

45 

46 

47 

48 

8 

5 1 

52 

53 

54 

55 

56 

u 

5 g 

6o 


Sine 


8 


8-940296 

941708 

943174 

944606 

946034 

947456 

948874 

950287 

951696 

953 ioo 

954499 

8- 955804 
957284 
958670 
960052 
961429 
962801 
964170 
965534 
966893 
968249 

969600 
970947 
972289 
973628 
974962 
976293 
977619 
978941 
980259 
981573 

982883 
984189 

985491 
986789 
988083 
989374 

990660 

991943 
993222 
994497 
995768 
997036 
998299 
999560 

9- 000816 
002069 
oo 33 i 8 
oo 4563 
oo 58 o 5 
007044 

9-008278 
009610 
010737 
011962 
oi3i82 
014400 
01 56 1 3 
016824 
01 8 o 3 1 
019235 


8 


8 


D. 


24 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

21 

21 

21 

21 

21 

21 

21 

21 

21 

21 

21 

21 

21 

21 

21 

21 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 


03 

94 

8 7 

79 
7 i 
63 
55 
48 
4 o 
32 
25 

17 

10 

02 

9 5 

88 

80 
73 
66 
5 9 
52 

44 

38 

3 i 

24 

17 

10 

o 3 

97 

9 ° 

83 

77 

70 

63 

57 

5 o 

44 

38 

3 i 

25 

19 

12 

06 

00 

94 

87 

82 

76 

7 ° 

64 

58 

52 

46 

40 

34 

29 

23 

17 

12 

06 

00 


Cosine 


Cosine 


D. 


9-998344 

998333 
998322 
998311 
998300 
998289 
998277 
998266 
998255 
998243 
998232 

9-998220 

998209 

99 8i 97 

998186 

998174 
998163 
9981 5 1 
998139 
998128 
998116 

9-998104 

998092 

998080 

998068 

998056 

998044 

998032 

998020 

998008 

997996 

9-997985 

997972 

997969 

997947 

997930 

997922 

997910 

997897 

997880 

997872 

9-997860 

997847 

997835 

997822 

997809 

997797 

997784 

997771 

997758 

997740 

9-997732 

997719 

997706 

997693 

997680 

997667 

997654 

997641 

997628 

997614 

Sine 


(84 DEGREES.) 







































24 (6 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

*7 

1*8 

'9 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

3 9 

40 

41 

42 

43 

44 

45 

46 

47 

48 

ll 

51 

52 

53 

54 

55 

56 

57 

58 

6? 

9-019235 

020435 

021632 

022825 

024016 

025203 

026386 

027567 

028744 

029918 

031089 

9-032257 
o33421 
034082 
035741 
036896 
c38o48 
o 3 9 i 97 
040342 
041485 
042625 

9-043762 

044895 

046026 

047104 

048279 

049400 

o5o5i9 

o 5 i 635 

052749 

o 53859 

9-054966 
056071 
057172 
058271 
059367 
060460 
061551 
062639 
063724 
064806 

9-o65885 

066962 

o68o36 

069107 

070176 

071242 

072306 

073366 

074424 

075480 

9-076533 

077583 

078631 

079676 

080719 

081759 

082797 

083832 

084864 

086894 

20-00 

I9.95 

19-89 

I9-84 

ig-lS 

19-73 

19-67 

19-62 

19A7 

19 • 5i 

19-47 

19-41 

19-36 

i9-3o 

19-25 

19-20 

19 • 15 
19-10 
I9 -o 5 
18.99 
18-94 

18-89 

18-84 

18-79 

18-75 

18-70 

18 - 65 
i8-6o 

18 • 55 
i8-5o 

18-45 

18 • 41 

18.36 

18 • 31 
18-27 

18 - 22 
18-17 
i8-13 
18-08 
18-04 
17-99 

17-94 

17-00 

17-86 

17-81 

17.77 

17.72 

17-68 

17-63 

'1-5? 

17-55 

I7-50 

I7-46 

17-42 

17-38 

17-33 

17-29 

17-25 

17-21 

17.17 

17. i3 

9-997614 

997601 

997588 

997574 

997561 

997547 

997534 

997520 

997507 

997493 

997480 

9•997466 

997462 

997439 

997426 

997411 

"7^97 

997383 

997669 

997355 

997341 

9-997327 
9973i3 
697209 
997285 
997271 

997 2 67 

997242 

997228 

997214 

997*99 

9-997185 

997*7° 
997156 
997141 
997127 
9971*2 
997008 
997083 
997068 
997053 

9-997039 

997024 

997009 

996994 

996979 

996964 

996949 

996934 

996919 

996904 

9-996889 

996874 

996858 

996843 

996828 

996812 

996797 

996782 

996766 

996751 

•22 

•22 

-22 

-22 

-22 

-22 

•23 

•23 

•23 

-23 

-23 

■23 

-23 

•23 

•23 

•23 

•23 

•23 

•23 

•23 

•23 

• 24 

• 24 
•24 

• 24 
*24 
•24 
•24 
•24 
•24 

• 24 

•24 

•24 

•24 

•24 

• 24 
•24 
•24 

•25 

-25 

•25 

•25 

•25 

•25 

•25 

•25 

•25 

• 25 
•25 
•25 
■25 

•25 

•25 

•25 

•25 

-25 

.26 

.26 

.26 

.26 

.26 

9-021620 

022834 

024044 

02525 i 

026455 

027655 

028852 

030046 

o 3 i 237 

o 32425 

033609 

9-03479* 

035969 
037144 
o383i6 
039485 
o4o65 1 
o 4 i 8 i 3 
042973 
04413o 
045284 

9 - 046434 
047582 
048727 
049869 
o5iooo 
052144 
053277 
054407 
o55535 
o5665g 

9-057781 
058900 
060016 
061i3o 
062240 
063348 
064453 
o65556 
o66655 
067762 

9-068846 

069938 

071027 

072113 

073*97 

074278 

075356 

076432 

077605 

078676 

9-079644 

080710 

081773 

082833 

083891 

084947 

086000 

087050 

088098 

089144 

20-23 
20-17 
20-1 I 

20-06 
20-00 
i 9 - 9 5 
19-90 
19-85 

19.79 

19-74 

19-69 

I9-64 

19.58 

19.53 

19-48 

19.43 
19*38 
I9-33 
19-28 
I9-23 
19-18 

19 -13 
19-08 
19.o3 
18-98 
18-93 

18-89 

18-84 

18.79 
18-74 
18-70 

18 -65 
18-69 

18 - 55 

18 • 51 
18-46 
18-42 
18-37 
i8-33 
18-28 
18-24 

18-19 

18 • 15 

18-10 
18-06 
18-02 

*7-97 

I7 -o 3 

17.89 

17-84 

17-80 

17.76 

17.72 

*7-67 

17-63 

17-59 

17.55 

17.51 

*7-47 

17.43 
17.38 

10-978380 

977166 

976956 

974749 

973540 

972345 

97**48 

969954 

960763 

967675 

966391 

10-966209 
964031 
962856 
961684 
960515 

959349 

958187 

967027 

955870 

954716 

io -953566 
952418 
961273 
95 oi 3 i 
948992 
947006 
946723 
945593 

944465 

943341 

10-942219 

941100 

939984 

938870 

937760 

936652 

935547 

934444 

933345 

932248 

10-931154 
930062 
928973 
927887 
926803 
925722 
924644 

923568 

922495 

921424 

10-920356 

919290 

918227 

9*7167 

916109 

9i5o53 

914000 

9*2950 

911902 

910866 

60 

5 9 

58 

57 

56 

55 

54 

53 

52 

5i 

5o 

49 

48 

47 

46 

45 

44 

43 

42 

4i 

40 

3 9 

38 

37 

36 

35 

34 

33 

32 

3i 

3o 

« 

20 

28 

27 

26 

25 

24 

23 

22 

21 

20 

10 

10 

*7 

16 

15 

14 

i3 

12 

11 

10 

7 

6 

5 

4 

3 

2 

1 

0 


Cosine 

D. 

Sine 

Cotan". 

D. 

Tang. 

M. 


(83 DEGREES.) 


























































SINES AND TANGENTS. (7 DEGREES.) 


25 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

0 

9-086894 

17 • i3 

9-996751 

-26 

9•089144 

17-38 

1 

086922 

17.09 

996735 

•26 

090187 

17.34 

2 

087947 

17-04 

996720 

• 26 

091228 

17-3o 

3 

088970 

17-00 

996704 

•26 

092266 

17-27 

4 

089990 

16-96 

996688 

•26 

093302 

17-22 

5 

091008 

16-92 

996673 

•26 

094336 

17-19 

6 

092024 

16-88 

996657 

•26 

095367 

17-10 

7 

093037 

16-84 

996641 

• 26 

096395 

17-11 

8 

094047 

16-80 

996626 

•26 

097422 

17-07 

9 

096066 

16-76 

996610 

•26 

098446 

17-o3 

10 

096062 

16-73 

996594 

• 26 

099468 

16-99 

11 

9-097065 

16-68 

9-996578 

.•27 

9-100487 

16-96 

12 

098066 

16-65 

996662 

•27 

ioi 5 o 4 

16-91 

i3 

099065 

16-61 

996646 

.27 

102519 

16-87 

14 

100062 

16-57 

996530 

.27 

io 3532 

16-84 

i5 

ioio 56 

16 • 53 

996614 

.27 

104642 

16-80 

16 

102048 

16-49 

996498 

.27 

io555o 

16-76 

*7 

io 3 o 37 

16-40 

996482 

•27 

io6556 

16-72 

18 

io 4 o 25 

16-41 

996465 

•27 

107559 

16-69 

*9 

10O010 

16 - 38 

996449 

•27 

io856o 

16-60 

20 

105992 

i 6-34 

996438 

.27 

109559 

16-61 

21 

9-106973 

i 6-3 o 

9-996417 

*27 

9-iio 556 

16-58 

22 

107961 

16-27 

996400 

• 27 

111551 

16-54 

23 

108927 

i 6-23 

996384 

• 27 

112543 

i6-5o 

24 

109901 

16-19 

996368 

•27 

113533 

16-46 

25 

110873 

16-10 

99&35 i 

•27 

114621 

i 6-43 

26 

111842 

16-12 

996335 

•27 

115607 

16-39 

27 

112809 

16-08 

996318 

•27 

116491 

16 • 36 

28 

113774 

i6-o5 

996302 

• 28 

117472 

l6*32 

29 

114737 

16-01 

996285 

.28 

118462 

16-29 

3o 

115698 

i 5-97 

996269 

•28 

119429 

16-20 

3i 

9-116656 

i 5-94 

9-996262 

.28 

9-120404 

i6- 22 

32 

117613 

15.90 

996235 

.28 

1-21377 

16 • 18 

33 

118667 

16*87 

996219 

.28 

122348 

16 -15 

34 

119619 

15 • 83 

996202 

.28 

123317 

16 • 11 

35 

120469 

i5-8o 

996185 

.28 

124284 

16-07 

36 

121417 

15-76 

996168 

• 28 

126249 

16-04 

37 

122362 

15 • 73 

996151 

• 28 

126211 

i6-oi 

38 

I233 o 6 

16-69 

996134 

• 28 

127172 

15 • 97 

3 9 

124248 

15-66 

996117 

-28 

128160 

i 5-94 

4o 

125187 

i 5-62 

996100 

• 28 

129087 

15-91 

4i 

9-126125 

i5-5g 

9-996083 

• 29 

9-i 3 oo 4 i 

15-87 1 

42 

127060 

15 - 56 

996066 

.29 

130994 

i 5-84 

43 

127993 

i5 - 52 

996049 

■ 29 

131944 

15 - 81 

44 

128925 

i 5-4 o 

996032 

•29 

132893 

15 • 77 

45 

129864 

15-45 

996016 

.29 

133839 

i 5-74 

46 

'130781 

15-42 

990998 

• 29 

134784 

15 - 71 

47 

131706 

15-39 

995980 

• 29 

135726 

16-67 

48 

i 3263 o 

i5-35 

996968 

•29 

136667 

i 5-64 

i 9 

13355i 

i 5-32 

996946 

• 29 

137606 

15 • 61 

5o 

134470 

i 5-29 

995928 

-29 

i 38542 

15-58 

5i 

9 -i 35387 

15 • 25 

9-996911 

.29 

9-139476 

15 - 55 1 

52 

i363o3 

15 • 22 

996894 

.29 

140409 

15 • 51 

53 

137216 

i5-19 

995876 

.29 

i 4 i 34 o 

i 5-48 

54 

138i28 

i5-16 

996869 

• 29 

142269 

i 5-45 

55 

139037 

15 • 12 

995841 

•29 

143196 

15-42 

56 

139944 

16-09 

995823 

-29 

144121 


57 

140860 

i 5 -o 6 

996806 

• 29 

146044 

i 5-3 o 

58 

141754 

i5-o3 

995788 

.29 

146966 

i 5-32 

5 9 

142655 

i5-oo 

99 5 77 1 

•29 

146885 

i 5-29 . 

60 

143555 

14-96 

995753 

-29 

147803 

15 • 26 


Cosine 

D. 1 

Sine 


Cotang. 

D. 


Cotang. 


10-910856 

909813 

908772 

907734 

906698 

905664 

904633 

9 o 36 o 5 

902678 

901554 

900532 

10-899513 
898496 
897481 
896468 
895458 
894460 

893444 


869691 
85866 o 
867731 
8568 o 4 
855879 
864966 
854 o 34 
853 11 5 
852197 


1 


60 

5 9 

58 

57 

56 

55 

54 

53 

52 

5 i 

5 o 

49 

48 

47 

46 

45 

44 

43 


892441 ! .42 
891440 41 

890441 40 

10-889444 39 

888449 ; 38 
887457 37 

886467 36 

885479 i 35 
* 884493 I 34 
883509 33 

882628 32 

881648 3 i 
880671 3 o 


878623 
877652 
876683 
875716 
874751 
873789 
872828 
871870 j 21 
870913 1 20 


20 

28 

27 

26 

25 

24 

23 

22 


869006 
868 o 56 ! i 
867107 
866161 ; i 5 
8652 i 6 14 

864274 i 1 3 
863333 
862395 
861408 




12 
11 


10 


7 

6 

5 

4 

3 

2 

1 

o 


Tang. M. 


(82 DEGREES.) 














































































26 


(8 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

1 

Cotang. 


0 

9 *x 43555 

14-96 

9*995753 

• 3 o 

9-147803 

1 5 • 26 

io- 852 I 97 

60 

i 

144453 

14-93 

995735 

• 3 o 

148718 

1 5 • 23 

85 1 282 

59 

2 

145349 

14-90 

995717 

• 3 o 

149632 

l 5-20 

85 o 368 

58 

3 

146243 

14-87 

995699 

• 3 o 

i 5 o 544 

1 5 • 17 

849406 

57 

4 

I 47 i 36 

14-84 

995681 

• 3 o 

1 5 1 454 

1 5 • 1 4 

848646 

56 

5 

148026 

14*81 

995664 

• 3 o 

152363 

1 5 - 11 

847637 

55 

6 

i 48 qi 5 

14-78 

995646 

• 3 o 

153269 

i 5 -o 8 

846731 

54 

7 

149002 

14-75 

995628 

• 3 o 

i 54 i 74 

i 5 -o 5 

845826 

53 

8 

i 5 o 686 

14-72 

995610 

• 3 o 

155077 

l 5-02 

844928 

52 

9 

1 5 i 56 g 

14-69 

995591 

• 3 o 

155978 

14-99 

844022 

5 i 

IO 

i 5245 i 

14-66 

995573 

• 3 o 

156877 

14-96 

843123 

5 o 

ii 

9*i 5333 o 

14*63 

9 * 9 q 5555 

• 3 o 

9-157775 

14-93 

10-842225 

49 

12 

1 54208 

14*60 

995537 

• 3 d 

158671 

14-90 

841329 

48 

i 3 

i 55 o 83 

i 4-57 

995519 

• 3 o 

1 69666 

14-87 

840435 

47 

14 

155967 

14-54 

9955 oi 

• 3 i 

160457 

14-84 

839548 

46 

i 5 

i 5683 o 

i 4 - 5 i 

995482 

• 3 i 

1 6 1 347 

i 4 - 8 i 

838653 

45 

16 

157700 

14-48 

995464 

• 3 i 

162236 

14-79 

837764 

44 

*7 

1 58569 

i 4-45 

995446 

• 3 i 

1 63123 

14-76 

S36877 

43 

18 

159435 

14-42 

995427 

• 3 i 

164008 

14-73 

835992 

42 


i 6 o 3 oi 

14-39 

996409 

• 3 i 

164892 

14-70 

835 io 8 

4 i 

20 

161164 

14-36 

995390 

• 3 i 

165774 

14-67 

834226 

4 o 

21 

9*162025 

i 4-33 

9-995372 

* 3 i 

9.i 66654 

14-64 

10-833346 

3 q 

22 

162885 

i 4 * 3 o 

995353 

• 3 i 

167532 

14-61 

832468 

38 

23 

163743 

14-27 

995334 

• 3 i 

168409 

i 4-58 

83 1 59 1 

37 

24 

164600 

14-24 

9953 i 6 

• 3 i 

169284 

14-55 

830716 

36 

25 

i 65454 

14-22 

995297 

• 3 i 

170157 

14-53 

829843 

35 

26 

166307 

14-19 

995278 

• 3 i 

171029 

i 4 - 5 o 

828971 

34 

27 

167169 

i 4 -16 

995260 

* 3 i 

171899 

14-47 

828101 

33 

28 

168008 

14-13 

995241 

•32 

172767 

14-44 

827233 

32 

29 

168856 

14-10 

996222 

*32 

• 173634 

14-42 

826366 

3 i 

3 o 

169702 

14-07 

990203 

*32 

174499 

14-39 

8255 oi 

3 o 

3 i 

9*170547 

i 4 -o 5 

9-995184 

•32 

9*175362 

14-36 

10-824638 

29 

32 

171389 

14-02 

9951 65 

•32 

176224 

14-33 

823776 

28 

33 

172230 

i 3-99 

996146 

•32 

177084 

i 4 - 3 i 

822916 

27 

34 

173070 

13-96 

996127 

•32 

177942 

14-28 

822058 

26 

35 

173908 

i 3 - 94 

996108 

*32 

178799 

14-25 

821201 

25 

36 

174744 

13-91 

995089 

*32 

179655 

14-23 

820345 

24 

37 

175578 

i 3-88 

995070 

*32 

i 8 o 5 o 8 

14-20 

819492 

23 

38 

176411 

1 3 • 86 

995 o 5 i 

•32 

181 36 o 

14-17 

8 1 8640 

22 

39 

177242 

1 3 • 83 

q 95 o 32 

•32 

182211 

14 -15 

817789 

21 

4 o 

178072 

i 3 - 8 o 

995 oi 3 

*32 

i 83 o 59 

14-12 

816941 

20 

4 i 

9*178900 

1 3 • 77 

9*994993 

*32 

9-183907 

14*09 

10-816093 

19 

42 

179726 

i 3 * 74 

994974 

*32 

184762 

14-07 

815248 

l8 

43 

i 8 o 55 i 

1 3 • 72 

994955 

•32 

185597 

14-04 

8 i 44 o 3 

17 

44 

181374 

13-69 

994935 

*32 

186439 

14-02 

8 1 356 1 

l6 

45 

182196 

1 3 • 66 

994016 

.33 

187280 

1 3 • 99 

812720 

l 5 

46 

i 83 oi 6 

i 3-64 

994896 

•33 

188120 

13*96 

811880 

14 

47 

183834 

i 3 - 6 i 

994877 

.33 

188958 

1 3 • 93 

811042 

i 3 

48 

i 8465 i 

1 3 • 5 g 

994857 

• 33 

189794 

13-91 

810206 

12 

49 

185466 

1 3 • 56 

994838 

• 33 

190629 

1 3 - 89 

809371 

11 

5 o 

186280 

i 3*53 

994818 

• 33 

191462 

1 3 • 86 

8 o 8538 

10 

5 i 

9*187092 

i 3 * 5 i 

9.994798 

• 33 

9-192294 

1 3 - 84 

10-807706 

Q 

52 

187903 

i 3*48 

994779 

•33 

193124 

1 3 • 81 

806876 

8 

53 

188712 

1 3 - 46 

994709 

• 33 

193953 

* 3-79 

806047 

7 

54 

189519 

1 3-43 

994739 

• 33 

194780 

1 3 - 76 

8 o 5220 

6 

55 

190325 

i 3 * 4 i 

994719 

• 33 

196606 

1 3 • 74 

804894 

5 

56 

191130 

1 3 - 38 

994700 

• 33 

196430 

1 3 • 71 

803570 

4 

5 7 

191933 

1 3 • 36 

994680 

• 33 

197253 

1 3 • 69 

802747 

3 

58 

192734 

1 3 • 33 

994660 

•33 

198074 

1 3 -66 

801926 

2 

59 

193534 

i 3 * 3 o 

994640 

• 33 

198894 

i 3-64 

801106 

1 

60 

194332 

1 3 - 28 

994620 

• 33 

199713 

1 3 • 61 

800287 

0 


Cosine 

D. 1 

Sine 


Cotang. 

D. 

Tang. 

M. 


(81 DEGREES.) 





















































SINES AND TANGENTS. (9 DEGREE.) 


27 


M. 

Sino 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9-194332 

i 3-28 

9-994620 

•33 

9-199713 

i 3-6 i 

10-800287 

60 

i 

196129 

i 3-26 

994600 

-33 

200629 

13 - 69 

799471 

5 9 

2 

19592a 

13 • 23 

99458o 

•33 

2 oi 345 

13 • 56 

798655 

5? 

3 

196719 

13 - 21 

99456o 

•34 

202159 

13 • 54 

797841 

57 

4 

197511 

13 • 18 

994540 

•34 

202971 

13 - 52 

797029 

56 

5 

198302 

13 • 16 

994519 

•34 

203782 

13 • 49 

796218 

55 

6 

199091 

i3-13 

994499 

•34 

204692 

13 - 47 

796408 

54 

7 

199879 

13 -11 

994479 

•34 

205400 

i 3-40 

794600 

53 

8 

200666 

i3-o8 

994459 

• 34 

206207 

i 3-42 

793793 

52 

9 

2 oi 45 i 

i3-o6 

994438 

•34 

207013 

i 3-4 o 

792987 

5i 

10 

202234 

i 3 -o 4 

9944 i 8 

-34 

207817 

i 3 - 38 

792183 

5o 

11 

9-203017 

i 3 -oi 

9-994397 

•34 

9-208619 

13 - 35 

10 - 791381 

49 

12 

203797 

12 ‘99 

994377 

• 34 

209420 

13 • 33 

790680 

48 

i3 

204577 

12-96 

994357 

•34 

210220 

13 • 31 

789780 

47 

14 

2o5354 

12-94 

994336 

•34 

211018 

i 3-28 

788982 

46 

i5 

2o6i3i 

1 2 -02 

9943i6 

-34 

211815 

i 3-26 

788186 

45 

16 

206906 

12-89 

994296 

•34 

212611 

i 3-24 

787389 

44 

*7 

207679 

12-87 

994274 

-35 

2i 34 o 5 

13 • 21 

786690 

43 

18 

208462 

12-85 

994254 

•35 

214108 

13 -19 

785802 

42 

l 9 

209222 

12-82 

994233 

•35 

214989 

13 • 17 

785011 

4i 

20 

209992 

I2-8o 

994212 

•35 

215780 

13 • 15 

784220 

40 

21 

9-210760 

12.78 

9-994191 

-35 

9-216568 

13 • 12 

10-783432 

3 9 

22 

211526 

12-75 

994171 

• 35 

217356 

i3-10 

782644 

38 

23 

212291 

12-73 

99415o 

• 35 

218142 

13 -08 

781858 

37 

24 

2i3o55 

12-71 

994129 

•35 

218926 

i3 -o5 

781074 

36 

25 

213818 

12-68 

994108 

• 35 

219710 

i3-o3 

780290 

35 

26 

214579 

12-66 

994087 

-35 

220492 

i 3 -oi 

779508 

34 

2 7 

215338 

12-64 

994066 

• 35 

221272 

12-99 

778728 

33 

28 

216097 

12-61 

994045 

• 35 

222052 

12-97 

777948 

32 

2 9 

216854 

12-59 

994024 

•35 

222830 

12-94 

777170 

3i 

3o 

217609 

12-57 

994 oo 3 

-35 

2236 o 6 

12-92 

776394 

3o 

3i 

9*2i8363 

12-55 

9-993981 

• 35 

9-224382 

12-90 

10-775618 

29 

32 

219116 

12-53 

993960 

-35 

225 i 56 

12-88 

774844 

28 

33 

219868 

I2-5 o 

993939 

•35 

226929 

12-86 

774071 

27 

34 

220618 

12-48 

993918 

-35 

226700 

12-84 

7733oo 

26 

35 

221367 

12-46 

993896 

-36 

227471 

12-81 

772529 

25 

36 

2221i5 

12-44 

993876 

-36 

228239 

12-79 

771761 

24 

3 7 

222861 

12-42 

993854 

-36 

229007 

12-77 

770993 

23 

38 

223606 

12*39 

998832 

-36 

229773 

12-75 

770227 

22 

3 9 

224349 

12-37 

993811 

-36 

23o539 

12-73 

769461 

21 

4o 

226092 

12*35 

993789 

-36 

231302 

12-71 

768698 

20 

4i 

9-225833 

12-33 

9-993768 

-36 

9-232 o 65 

12-69 

10-767935 

IO 

42 

226573 

12 • 31 

993746 

-36 

232826 

12-67 

767174 

l8 

43 

227311 

12-28 

99 3 725 

-36 

233586 

12-65 

766414 

17 

44 

228048 

12-26 

993703 

-36 

234345 

12-62 

765655 

l6 

45 

228784 

12-24 

993681 

•36 

235 io 3 

12-60 

764897 

i5 

46 

229518 

12-22 

993660 

-36 

235859 

12-58 

764141 

i4 

47 

230252 

12-20 

993638 

-36 

236614 

12-56 

763386 

i3 

48 

230984 

12- l8 

993616 

-36 

23 7 368 

12-04 

762632 

12 

49 

231714 

12- l6 

993594 

.37 

238120 

12-52 

761880 

11 

5o 

232444 

12- 14 

993572 

.37 

238872 

12-5 o 

761128 

10 

5i 

9-233172 

12-12 

9-99355o 

•37 

9-239622 

12-48 

10-760378 

9 

52 

233899 

I2-09 

993528 

.37 

240371 

12-46 

759629 

8 

53 

234626 

12-07 

9935o6 

•37 

241118 

12-44 

758882 

7 

54 

235349 

12-05 

993484 

.37 

• 241865 

12-42 

7 58135 

6 

55 

236073 

I 2 • o3 

993462 

.37 

242610 

12-40 

757390 

5 

56 

^36795 

12-01 

998440 

.37 

243354 

12-38 

766646 

4 

57 

2 3 7 515 

11.99 

993418 

.37 

244097 

12-36 

755903 

3 

58 

238235 

II-97 

993396 

-3 7 

244839 

12-34 

755i6i 

2 

5 9 

238953 

11-95 

993374 

•37 

240079 

12-32 

704421 

1 

6 o 

239670 

11 -93 

99335 i 

.37 

246319 

I2-3 o 

7 5368 i 

0 


Cosine 

D. 

Sine 


Cotang. 

D. 

Tang. 

M. 


(80 DEGREES.) 



















































28 (10 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

I). 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9-239670 

11-93 

9 - 99335 i 

• 37 

9-246319 

I 2 - 3 o 

10-753681 

60 

i 

24o386 

11-91 

993329 

•37 

247057 

12-28 

752943 

kJ Q 

2 

241101 

11-89 

993307 

.37 

247794 

12-26 

762206 

58 

3 

241814 

11-87 

993285 

.37 

24853 o 

12-24 

761470 

57 

4 

242526 

n -85 

993262 

- 3 7 

249264 

12-22 

7607.36 

56 

5 

243237 

n -83 

993240 

.37 

249998 

12-20 

760002 

55 

6 

243947 

11 • 81 

993217 

-38 

250760 

I 2 • 18 

749270 

54 

7 

244606 

n -79 

993196 

-38 

261461 

12- 17 

748539 

53 

8 

245363 

n -77 

993172 

-38 

262191 

12- l6 

747809 

52 

9 

246069 

11-75 

993149 

• 38 

262920 

1 2 • 13 

747080 

5 i 

IO 

24677O 

11-73 

993127 

-38 

253648 

12-11 

746352“ 

5 o 

n 

9-247478 

11-71 

9-993104 

• 38 

9-254374 

12-09 

10-745626 

49 

12 

248181 

11-69 

993081 

-38 

255 ioo 

12-07 

744900 

48 

i 3 

248883 

11-67 

993059 

•38 

255824 

I 2 • 06 

744176 

47 

14 

249583 

11 -65 

993036 

-38 

256547 

12 -o 3 

743453 

46 

i 5 

250282 

n -63 

993 oi 3 

-38 

257269 

12-01 

742731 

45 

16 

250980 

11 -6i 

992990 

•38 

257990 

12-00 

742010 

44 

17 

251677 

ii- 5 9 

992967 

•38 

268710 

11-98 

741290 

43 

18 

252373 

ii -58 

992944 

-38 

269429 

11-96 

740571 

42 

19 

253067 

n -56 

992921 

-38 

260146 

11-94 

739864 

4 i 

20 

253761 

u -54 

992898 

• 38 

260863 

I 1 -92 

739137 

4 o 

21 

9-254453 

11-52 

9-992875 

-38 

9-261578 

1 I -00 

10-738422 

3 9 

22 

255 i 44 

11 -5o 

992862 

-38 

262292 

11-89 

737708 

38 

23 

255834 

11-48 

992829 

- 3 9 

263 oo 5 

11-87 

736995 

37 

24 

256523 

11-46 

992806 

- 3 9 

263717 

n -85 

736283 

36 

25 

257211 

u -44 

992783 

• 3 9 

264428 

n -83 

735572 

35 

26 

257898 

11-42 

992759 

•39 

265 1 38 

11 • 81 

734862 

34 

27 

258583 

11 • 41 

992736 

• 3 9 

265847 

ii *79 

734 i 53 

33 

28 

259268 

11 -39 

992713 

- 3 9 

266555 

11-78 

733445 

32 

29 

259951 

11-37 

992690 

• 3 9 

267261 

11-76 

732739 

3 i 

3 o 

26o633 

n -35 

992666 

• 3 9 

267967 

11-74 

732033 

3 o 

3 i 

9•261 3 14 

11 -33 

9-992643 

- 3 9 

9-268671 

11-72 

10-731329 

29 

32 

261994 

11 • 3 1 

992619 

- 3 9 

269375 

11-70 

730626 

28 

33 

262673 

11 - 3 o 

992596 

• 3 9 

270077 

11-69 

729923 

27 

34 

26335 i 

11-28 

992572 

- 3 9 

270779 

11-67 

729221 

26 

35 

264027 

11-26 

992549 

• 3 9 

27U79 

u -65 

728521 

26 

36 

264708 

11-24 

992020 

• 3 9 

272178 

11-64 

727822 

24 

37 

265877 

11-22 

992601 

- 3 9 

272876 

11-62 

727124 

23 

38 

266 o 5 1 

11-20 

992478 

*40 

273573 

11 - 6o 

726427 

22 

3 9 

266723 

II-I9 

992454 

• 40 

274269 

n -58 

725731 

21 

4 o 

267895 

II-I 7 

992430 

• 40 

274964 

11-57 

725 o 36 

20 

4 i 

9-268065 

11 ■ 15 

9-992406 

•40 

9-275658 

n -55 

10-724342 

19 

42 

268734 

11 • i 3 

992382 

•40 

276351 

n -53 

723649 

l8 

43 

269402 

11 • 11 

992359 

• 40 

277043 

11 • 5 1 

7 2 ?-957 

17 

44 

270069 

11 • 10 

992335 

•40 

277734 

11 - 5 o 

722266 

l6 

45 

270730 

11 - 08 

992311 

• 40 

278424 

11 -48 

721576 

i 5 

46 

271400 

11 - 06 

992287 

•40 

2791i 3 

11 *47 

720887 

i 4 

47 

272064 

11 -o 5 

992263 

•40 

279801 

11 -45 

720199 

i 3 

48 

272726 

11 -o 3 

992239 

•40 

280488 

ii -43 

7i 9 5 i2 

12 

49 

273388 

I I -01 

992214 

•40 

281174 

11 - 41 

718826 

11 

5 o 

274049 

10.99 

992190 

•40 

281858 

11 - 4 o 

718142 

10 

5 i 

9-274708 

10-98 

9-992166 

• 40 

9-282542 

11 -38 

10-717458 

0 

52 

275867 

10-96 

992142 

•40 

283225 

11 -36 

716775 

8 

53 

276024 

10-94 

992117 

• 4 i 

283907 

11 -35 

716093 

7 

54 

276681 

10-92 

992098 

•41 

284688 

n -33 

715412 

6 

55 

277337 

10-91 

992069 

• 4 i 

286268 

11 • 3 1 

714732 

5 

56 

277991 

10-89 

992044 

• 4 i 

286947 

11 - 3 o 

714063 

4 

57 

278644 

10-87 

992020 

• 4 i 

286624 

11-28 

713376 

3 

58 

279297 

io-S6 

99 1 996 

•41 

287301 

11-26 

712690 

2 

5 9 

279948 

10-84 

99 1 97 1 

• 4 i 

287977 

11-25 

712020 

1 

60 

280699 

10-82 

_ 

991947 

•41 

288662 

11-23 

711348 

0 


Cosine 

D. 

Sine 

Cotang. 

D. 

Tang. 

M. 


(79 DEGREES.) 




























































SINES AND TANGENTS. (11 DEGREES.) 29 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

1 3 

14 

1 5 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

IS 

3 1 

32 

33 

34 

35 

36 

3 7 

38 

3 9 

4 0 

41 

42 

43 

44 

45 

46 

47 

48 

49 

5 0 

5 1 

52 

53 

54 

55 

56 

5 7 

58 

5 9 

60 

9*280599 

281248 

281897 

282544 

283190 

283836 

284480 

285124 

285766 

286408 

2S7048 

9-287687 

288326 

288964 

289600 

290236 

290870 

291504 

292137 

292768 

293399 

9-294029 
2 9 4658 
295286 
295913 
296539 
297164 
297788 
298412 
299034 
299655 

9*300276 
300895 
3 oi 5 i 4 
3 o 2132 
302748 
3 o 3364 
303979 
304693 
3 o 5207 
3 o 58 i 9 

9 * 3 o 643 o 

307041 

307650 

308269 

308867 

309474 

3 10080 
3 io 685 
311289 
311893 

9*312495 

313097 

3 1 36 9 8 
314297 
314897 

3 15495 

3 16092 
316689 

317284 

317879 

10-82 

io-8i 

io *79 

io *77 

10-76 

10*74 

10*72 

10*71 

10-69 

10*67 

io-66 

10*64 

io *63 

io*6i 

10 - 5 o 
io *58 
io *56 
io -54 
Io -53 
io- 5 i 
io- 5 o 

10*48 

10*46 

10*45 

10*43 

10*42 

io*4o 

10-39 

10-37 

io *36 

io *34 

10*32 

io* 3 i 

10-20 

10-28 

10-26 

10-25 

10-23 

10-22 

• 10*20 
io* 19 

10-17 

10- 16 
io-14 
io* i 3 

10- I I 

10- 10 
10*08 
10*07 
io-o 5 
10*04 

io*o 3 

10*01 

10*00 

9*98 

9*97 

9*96 

9.94 

9 * 9 3 

9*91 

9.90 

9*991947 

991922 

991897 

991873 

991848 

991823 

991799 

991774 

991749 

991724 

991699 

9 * 99 i 674 
99 1 649 
991624 
991599 
99 i 574 
991649 
991524 
991498 
991473 
991448 

9*991422 

991397 

991372 

991346 

991321 

991295 

991270 

991244 

991218 

991193 

9-991167 

99 ii 4 i 

991115 

991090 

991064 

99 io 38 

991012 

990986 

990960 

990934 

9-990908 

990882 

990855 

990829 

990803 

990777 

990750 

990724 

990697 

990671 

9-990644 

990618 
990591 
990565 
990538 
990611 
990486 
990468 
990431 
9904^4 

•41 

•41 

• 4 i 

• 4 i 

• 4 i 

• 41 
•41 

•42 

• 42 

• 42 
•42 

•42 

•42 

•42 

•42 

•42 

•42 

•42 

•42 

•42 

•42 

•42 

• 42 
•43 
•43 
•43 
•43 
•43 
•43 
•43 
•43 

•43 

•43 

•43 

•43 

•43 

•43 

•43 

•43 

•43 

•44 

•44 

•44 

•44 

•44 

•44 

•44 

•44 

•44 

•44 

•44 

•44 
•44 
•44 
•44 
•44 
•45 
•45 j 
*45 1 
•45 ! 

• 45 

9-288652 

289326 

289999 

290671 

291342 

292013 

292682 

293350 

294017 

294684 

295349 

9-296013 

296677 

297369 

298001 

298662 

299322 

299980 

3 oo 638 

301296 

301961 

9-302607 

3 o 326 i 

303914 

304067 

3 o 52 i 8 

3 o 5869 

3 o 65 i 9 

307168 

307815 

308463 

9*309109 
309754 
310698 
3 i1042 

3 11 685 
312327 
312967 
3 i 36 o 8 
3 i 4247 

3 14885 

9• 3 1 5523 

3 161 5 o 
316795 
317460 

3 18064 
318697 
319329 
319961 
320692 
321222 

9 * 32 i 85 i 
322479 
323 io 6 
323733 
324658 
324983 
326607 
32623 i 
326853 
327470 

11-23 

11-22 

11*20 

II • l8 
11*17 

11 • 15 

11 • 14 
11*12 

II • 11 
Il-Og 
11-07 

ii *06 

11 - o 4 

11 - o 3 

I I -01 

II - 00 
10-98 
10-96 
10-95 
10-93 
10-92 

10*90 

10-89 

10-87 

io*86 

10*84 

io *83 

io*8i 

io-8o 

10-78 

io *77 

10*75 

10*74 

10-73 

10-71 

10-70 

io-68 

10-67 

io*66 

10-64 

10*62 

io*6i 

io-6o 

io -58 

10-57 

io *56 

io -54 

io -53 

io* 5 i 

io* 5 o 

10*48 

io *47 

io -45 

io -44 

io -43 

10-41 

10-40 

10-39 

10 - 3*7 

io -36 

io -35 

10*711348 

710674 

710001 

709329 

708658 

707987 

707618 

706600 

705983 

705616 

704651 

10-703987 

703623 

702661 

701999 

701638 

700678 

700020 

690362 

698705 

698049 

10-697393 

696769 

696086 

695433 

694782 

694131 

693481 

692832 

692185 

691537 

10-690891 
690246 
689602 
688968 
6883 1 5 
687673 
687063 
686392 
685763 
685 11 5 

10-684477 

683841 

683205 

682570 

681966 

68 i 6 o 3 

680671 

680069 

679408 

678778 

10-678149 

677521 

676894 

676267 

675642 

675017 

674396 

673769 

673147 

672626 

60 

57 

56 

55 

54 

53 

52 

5 i 

5 o 

49 

48 

47 

46 

45 

44 

43 

42 

4 i 

4 o 

39 

38 

37 

36 

35 

34 

33 

32 

3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

10 

17 

l 6 

i 5 

14 

i 3 

12 

11 

10 

7 

6 

5 

4 

3 

2 

1 

0 


Cosine 

D. : Sine | 1 Cotang. 

D. 

Tang. I M. 


(78 DEGREES.) 



















































30 (12 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-317879 

9-90 

9•990404 

•45 

9-327474 

io -35 

10-672526 

60 

i 

3 i 84?3 

9-88 

990378 

•45 

328096 

io -33 

671905 

5 9 

2 

3 19066 

9-87 

9903 5 1 

•45 

328716 

10-32 

671285 

58 

3 

319658 

9-86 

990324 

-45 

329334 

io- 3 o 

670666 

57 

4 

320249 

9-84 

990297 

•45 

329953 

10-20 

670047 

56 

5 

320840 

9-83 

990270 

• 45 

330070 

10-28 

669430 

55 

6 

32 i 43 o 

9-82 

990243 

-45 

331187 

10-26 

66881 3 

54 

7 

322019 

9-80 

99021 5 

•45 

33 i 8 o 3 

10-25 

668197 

53 

8 

322607 

9-79 

990188 

•45 

3324 i 8 

10-24 

667582 

52 

9 

323194 

9-77 

990161 

•45 

333 o 33 

10-23 

666967 

5 i 

IO 

323780 

0-76 

990134 

•45 

333646 

10-21 

666354 

5 o 

ii 

9*324366 

9.75 

9-990107 

.46 

9*334259 

10-20 

10-665741 

49 

12 

324956 

9-73 

990079 

-46 

334871 

10-19 

665 129 

48 

i 3 

325534 

9-72 

990062 

.46 

335482 

10-17 

6645 i 8 

47 

14 

326117 

9-70 

990026 

.46 

336098 

10- 16 

663907 

46 

i 5 

326700 

9-69 

989997 

•46 

336702 

io -15 

663298 

45 

16 

• 327281 

9.68 

989970 

•46 

3373 ii 

io -13 

662689 

44 

1 1 

327862 

9-66 

989942 

•46 

337919 

10-12 

662081 

43 

18 

328442 

9-65 

989910 

•46 

338527 

IO- I I 

661473 

42 

i 9 

329021 

9-64 

989887 

-46 

339 i 33 

IO- IO 

660867 

4 i 

20 

329699 

9-62 

989860 

•46 

339789 

10-08 

660261 

40 

21 

9-330176 

9-61 

9-989832 

-46 

9- 34 o 344 

10-07 

io- 65 g 656 

3 9 

22 

33 o 753 

9-60 

989804 

•46 

340948 

10-06 

65 go 52 

38 

23 

33 1329 

9-58 

989777 

-46 

34 i 552 

10-04 

658448 

37 

24 

331908 

9.57 

989749 

•47 

342 i 55 

io-o 3 

657845 

36 

25 

332478 

9-56 

989721 

•47 

342767 

10-02 

657243 

35 

26 

333 o 5 i 

9-54 

989693 

•47 

343358 

10-00 

656642 

34 

27 

333624 

9-53 

989665 

•47 

343958 

9*99 

656 o 42 

33 

28 

334195 

9-52 

989637 

*47 

344558 

9-98 

655442 

32 

29 

334766 

9 - 5 o 

989609 

•47 

345 i 57 

9'97 

654843 

3 i 

3 o 

335337 

9.49 

989582 

*47 

345755 

9 ' 9 6 

654245 

3 o 

3 i 

9-335906 

9-48 

9-989553 

•47 

9-346353 

9.94 

io -653647 

29 

32 

336475 

9-46 

989525 

•47 

346949 

9 ' 9 3 

653 o 5 i 

28 

33 

337043 

9-45 

989497 

*47 

347545 

9-92 

652455 

27 

34 

337610 

9-44 

989469 

•47 

348141 

9-91 

65 1 85 g 

26 

35 

338176 

9.43 

989441 

•47 

348735 

9-oo 

65 i 26 o 

25 

36 

338742 

9-41 

989413 

•47 

349329 

9-88 

650671 

24 

37 

339306 

9-40 

989384 

•47 

349922 

9-87 

650078 

23 

38 

339871 

9.39 

989356 

*47 

35 o 5 i 4 

9-86 

649486 

22 

3 9 

340434 

9-37 

989828 

•47 

35 1106 

9-85 

648894 

21 

40 

340996 

9-36 

989300 

•47 

351697 

9-83 

6483 o 3 

20 

41 

9• 34 i 558 

9-35 

9-989271 

•47 

9-302287 

9-82 

io- 6477 i 3 

IO 

42 

342119 

9-34 

989243 

•47 

352876 

9-81 

647124 

10 

43 

342679 

9-32 

9S9214 

•47 

353465 

9-80 

646535 

n 

44 

343239 

9 • 3 1 

989186 

'47 

354 o 53 

9'79 

645947 

16 

45 

343797 

9 - 3 o 

989157 

'47 

354640 

9'77 

645360 

i 5 

46 

344355 

9.29 

989128 

-48 

355227 

9-76 

644773 

14 

47 

344912 

9-27 

989100 

•48 

3558 i 3 

9-75 

644187 

i 3 

48 

345469 

9-26 

989071 

•48 

3563 g 8 

9*74 

643602 

12 

49 

346024 

9-25 

989042 

-48 

356982 

9 ' 7 3 

643 oi 8 

11 

5 o 

346579 

9-24 

989014 

-48 

35 7 o 66 

9 ’ 7 i 

642434 

10 

5 i 

9 • 347 1 34 

9-22 

9-988985 

-48 

9• 358 i 49 

9-70 

io- 64 i 85 i 

Q 

52 

347687 

9-21 

988956 

•48 

35873 i 

9-60 

641269 

8 

53 

348240 

9-20 

988927 

-48 

3 5 g 3 1 3 

9-68 

640687 

7 

54 

348792 

9.19 

988898 

-48 

869898 

9-67 

640107 

6 

55 

349343 

9 * 1 7 

988869 

•48 

36 o 474 

9-66 

639526 

5 

56 

349893 

9-16 

988840 

•48 

36 io 53 

9*65 

638947 

4 

57 

35 o 443 

9 • 1 5 

988811 

•49 

861682 

9-63 

638368 

3 

58 

300992 

9-14 

988782 

•49 

362210 

9-62 

637790 

2 

5 9 

301040 

9-13 

988753 

•49 

362787 

9-61 

6372 i 3 

1 

60 

302088 

9.11 

988724 

.49 

363364 

9-60 

636636 

0 


Cosine 

D. 

Sine 

Cotang. 

D. 

Tang-.. 

M. 


(77 DEGREES.) 









































SINES AND TANGENTS. (13 DEGREES.) 81 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

i D - 

Cotang. 


0 

9-352088 

g 

9*988724 

•49 

9*363364 

9* 60 

io*636636 

60 

i 

352635 


988695 

.49 

363940 

9*69 

636o6o 

5 9 

2 

353181 

9W ; 

988666 

.49 

364515 

9*58 

635485 

58 

3 

353726 

9*08 

988686 

•49 

365090 

9.57 

634910 

57 

4 

354271 

9*07 

988607 

.49 

365664 

9-55 

634336 

56 

5 

3548 i 5 

9 *o 5 

988578 

.49 

366237 

9*54 

633763 

55 ' 

6 

355358 

9* 04 

988548 

.49 

366810 

9*53 

633190 

54 

7 

355901 

9 *o 3 

9^19 

• 49 

367382 

9A2 

632618 

53 

8 

356443 

9*02 

988489 

.49 

36-^53 

9 ■ 51 

632047 

52 

9 

356984 

0*01 

988460 

• 49 

368524 

9*5o 

631476 

5i 

10 

357624 

8*99 

988480 

• 49 

869094 

9-49 

630906 

5o 

11 

9 -358o64 

8*98 

9*988401 

•49 

9O69663 

9-48 

io* 63 o 337 

49 

12 

3586o3 

8*97 

988371 

.49 

370232 

9*46 

629768 

48 

i3 

359141 

8*96 

988342 

•49 

370799 

9*45 

629201 

47 

14 

369678 

8*95 

988312 

•5o 

371367 

9.44 

628633 

46 

i5 

360215 

8* 9 3 

988282 

• 5o 

371936 

9.43 

628067 

45 

16 

360752 

8*92 

988252 

• 5o 

372499 

9-42 

627601 

44 

1 1 

361287 

8*91 

988223 

• 5o 

373064 

9*41 

626936 

43 

18 

361822 

8*90 

988 1 9 3 

• 5o 

373629 

9*40 

626371 

42 

1 9 

362356 

8*89 

988168 

•5o 

374196 

9*39 

625807 

41 

20 

362889 

8*88 

9 88l33 

•5o 

374766 

9*38 

625244 

40 

21 

9*363422 

8*87 

9*988103 

•5o 

9-375319 

9-37 

10*624681 

39 

22 

368904 

8*85 

988078 

•5o 

3 7 588 i 

9*35 

624119 

38 

23 

364485 

8*84 

988043 

*5o 

376442 

9-34 

623558 

37 

24 

365oi6 

8*83 

988018 

• 5o 

377003 

9-33 

622997 

36 

25 

365546 

8*82 

987988 

*5o 

877568 

9*32 

622437 

35 

26 

366075 

8-81 

987953 

• 5o 

378122 

9 • 31 

621878 

34 

2 7 

3666o4 

8* 80 

987922 

• 5o 

378681 

9-3 o 

621319 

33 

28 

367131 

8*79 

987892 

*5o 

379239 

9-29 

620761 

32 

29 

367659 

8*77 

987862 

*5o 

379797 

* 9-28 

620203 

3i 

3o 

368i85 

8*76 

987832 

• 5i 

38 o 354 

9.27 

619646 

3o 

3i 

9*368711 

8*75 

9*987801 

• 5i 

9*380910 

9-26 

10*619090 

29 

32 

369236 

8*74 

9 8 777! 

• 5i 

381466 

9-25 

6 i 8534 

28 

33 

369761 

8 • 73 

987740 

• 5i 

382020 

9*24 

617980 

27 

34 

370285 

8*72 

087710 

• 5i 

382575 

9*23 

617425 

26 

35 

370808 

8*71 

987679 

• 5i 

383i29 

9.22 

616871 

25 

36 

37i33o 

8*70 

987649 

• 5i 

383682 

9*21 

6 1 63 1 8 

24 

37 

371852 

8*69 

987618 

*5i 

384234 

9-20 

615766 

23 

38 

372373 

8*67 

987588 

*5i 

384786 

9-io 

615214 

22 

3 9 

372894 

8*66 

987557 

*5i 

385337 

9-i8 

614663 

21 

4o 

373414 

8*65 

987526 

• 5i 

385888 

9.17 

614112 

20 

4i 

9*373933 

8*64 

9*987496 

*5i 

9-386438 

9 • 15 

io* 6 i 3562 

J 9 

42 

374452 

8*63 

987465 

• 5i 

386987 

9*14 

6 i 3 oi 3 

18 

43 

37497 0 

8*62 

987434 

• 5i 

3S 7 d 36 

9-13 

612464 

17 

44 

375487 

8-61 

987403 

•52 

388084 

9*12 

611916 

l6 

45 

376003 

8* 60 

687372 

•52 

38863i 

9*ii 

611869 

i5 

46 

376519 

8*09 

987341 

•52 

389178 

9*io 

610S22 

14 

47 

377030 

8*58 

987310 

•52 

389724 

9.00 

610276 

i3 

48 

377549 

8*57 

987279 

•52 

390270 

9-08 

609760 

12 

49 

378063 

8*56 

987248 

•52 

390S15 

9-07 

609186 

11 

5o 

378577 

8*54 

987217 

•52 

391360 

9-06 

608640 

10 

5i 

9*379089 

8*53 

9*987186 

•52 

9-391903 

9 *o 5 

10*608097 

9 

52 

379601 

8*52 

987155 

• 62 

392447 

9-04 

607556 

8 

53 

38oii3 

8 - 51 

987124 

•52 

392989 

9 -o3 

607011 

7 

54 

380624 

8*5o 

987092 

•52 

393o3i 

9*02 

606469 

6 

55 

331134 

8.49 

987061 

•52 

394073 

9-01 

606927 

5 

56 

38 i 643 

8*48 

987030 

•52 

394614 

9-00 

6 o 5386 

4 

57 

382152 

8*47 

986998 

•52 

396154 

8-99 

604846 

3 

58 

382661 

8*46 

986967 

•52 

395694 

8.98 

6o4306 

2 

5 9 

383168 

8*45 

986936 

•52 

396263 

8*97 

603767 

1 

60 

383675 

8*44 

986904 

•52 

396771 

8*96 

6o322 9 

0 

Cosine 

D. 

• Sine 1 


Cotang. 

D. 

Tang. 

M. 


26 (76 DEGREES.) 























































32 (14 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

1 

Cotang. 


0 

9 * 383675 

8*44 

9*986904 

•52 

9-396771 

8-96 

10-603229 

60 

i 

384182 

8*43 

98687 3 

*53 

397309 

8.96 

602691 

5 9 

2 

384687 

8*42 

986841 

•53 

397846 

8-90 

6021 54 

58 

3 

385192 

8 * 4 i 

986809 

*53 

3 9 8383 

8-94 

601617 

5 ? 

4 

385697 

8* 40 

986778 

• 53 

398919 

8- 9 3 

601081 

56 

5 

386201 

8 • 3 o 

986746 

*53 

399455 

8-92 

6 oo 545 

55 

6 

386704 

8*38 

986714 

•53 

399990 

8-91 

600010 

54 

7 

387207 

8*37 

986683 

■ 53 

4 oo 524 

8-90 

699476 

53 

8 

387709 

8*36 

9^665 1 

*53 

4 oio 58 

n'n 9 

598942 

52 

9 

388210 

8*35 

986619 

•53 

401691 

8-88 

598409 

5 i 

IO 

388711 

8*34 

986587 

*53 

402124 

8-87 

597876 

5 o 

11 

9*389211 

8*33 

9*986555 

• 53 

9-402666 

8-86 

10*597344 

49 

12 

3897I 1 

8*32 

986628 

• 53 

403187 

8-85 

596813 

48 

i 3 

390210 

8 • 3 1 

98649i 

• 53 

403718 

8-84 

596282 

47 

14 

390708 

8 * 3 o 

986469 

•53 

404249 

8-83 

5 g 575 i 

46 

i 5 

391206 

8*28 

986427 

• 53 

404778 

8-82 

595222 

45 

16 

391703 

8 • 27 

986896 

•53 

4 o 53 o 8 

8-81 

594692 

44 

17 

392199 

8*26 

986363 

•54 

4 o 5836 

8-80 

594164 

43 

18 

392690 

8*25 

98633 i 

•54 

406364 

8.70 

5 9 3636 

42 


393191 

8*24 

986299 

• 54 

406892 

8-78 

693108 

4 i 

20 

3 9 3685 

8*23 

986266 

•54 

407419 

8-77 

592581 

40 

21 

9*394179 

8*22 

9*986234 

•54 

9-407945 

8-76 

10-692055 

39 

22 

394673 

8*21 

986202 

• 54 

408471 

8-75 

691529 

38 

23 

3 g 5 i 66 

8*20 

986169 

*54 

408997 

8-74 

591003 

3 7 

24 

3 9 5658 

8* 19 

986137 

• 54 

409621 

8-74 

5 qo 479 

36 

25 

3 g 6 i 5 o 

8-18 

986104 

*54 

410045 

8*73 

589960 

35 

26 

396641 

8*17 

986072 

• 54 

410569 

8-72 

589431 

34 

27 

397132 

0' 17 

986039 

•64 

411092 

8-71 

588908 

33 

28 

397621 

8* 16 

986007 

•54 

41161 5 

8-70 

588385 

32 

29 

3 q 8 i11 

8 • 1 5 

986974 

•64 

412137 

8-69 

58 7 863 

3 i 

3 o 

398600 

8* 14 

986942 

•54 

412658 

8-68 

587342 

3 o 

3 i 

9*399088 

8 • 1 3 

9*986909 

• 55 

9• 4 i 3 179 

8-67 

io-58682i 

29 

32 

399575 

8*12 

986876 

• 55 

413699 

8-66 

5863 oi 

28 

33 

400062 

8*ii 

986848 

• 55 

414219 

8-65 

585781 

27 

34 

4 oo 54 o 

8*io 

9 858 ii 

• 55 

414738 

8-64 

585262 

26 

35 

4 oio 35 

8*09 

986778 

• 55 

41 5 2 5 7 

8-64 

584743 

25 

35 

4 oi 52 o 

8* 08 

985745 

• 55 

4 i 5775 

8-63 

584225 

24 

-‘7 

4 o 2 oo 5 

8*07 

986712 

• 55 

416293 

8-62 

583707 

23 

38 

402489 

8*o6 

985679 

• 55 

416810 

8 • 6 1 

583190 

22 

3 9 

402972 

8 *o 5 

986646 

• 55 

417326 

8-60 

582674 

21 

4 o 

4 o 3455 

8*04 

985618 

• 55 

417842 

8-59 

582 1 58 

20 

4 i 

9*403938 

8 *o 3 

9*98558o 

• 55 

9•41 8358 

8-58 

10-581642 

! 9 

42 

404420 

8*02 

985547 

*55 

418873 

8 • 67 

58 1127 

l8 

43 

404901 

8*oi 

986614 

• 55 

419387 

8-56 

58 o 6 i 3 

17 

44 

4 o 5382 

8*oo 

985480 

• 55 

419901 

8-55 

580099 

l6 

45 

406862 

7-99 

985447 

• 55 

42 o 4 i 5 

8-55 

579580 

i 5 

46 

4 o 634 i 

7.98 

986414 

• 56 

420927 

8-54 

570073 

i 4 

47 

406829 

7-97 

9 8538 o 

• 56 

421440 

8*53 

578660 

i 3 

48 

407299 

7*96 

985347 

•56 

421962 

8-52 

578048 

12 

49 

407777 

7*95 

986814 

• 56 

422463 

8 • 5 i 

577537 

11 

5 o 

408254 

7-94 

985280 

•56 

422974 

8 - 5 o 

577026 

10 

5 i 

9*408731 

7-94 

9*985247 

• 56 

9-423484 

8.49 

10-576516 

0 

52 

409207 

7.98 

985218 

• 56 

423993 

8.48 

576007 

3 

53 

409682 

7.92 

985180 

• 56 

424003 

8.48 

676407 

7 

54 

410157 

7 - 9 1 

985146 

•56 

426011 

8-47 

574989 

6 

55 

4 io 632 

7*90 

9S5ii 3 

• 56 

426619 

8.46 

674481 

5 

56 

411106 

7*89 

986079 

•56 

426027 

8-45 

673973 

4 

57 

411579 

7*88 

986040 

• 56 

426034 

8-44 

573466 

3 

58 

4i2062 

7*87 

9860.1 

•56 

427041 

8-43 

572969 

2 

5 9 

412624 

7*86 

984978 

• 56 

427647 

8-43 

572453 

1 

60 

412996 

7*85 

984944 

•56 

428 o 52 

8-42 

571948 

0 


Cosine 

D. 

Sine 

1 

Cotang. 

D. 

Tang. 

M. 


(75 DEGREES.) 

































































SINES AND TANGENTS. (15 DEGREES.) 33 


M. 

Sine 

D. 

Cosine 

D. 

Tang. * 

D. 

Cotang. 


o 

9-412996 

7-85 

9-984944 

.57 

9-428052 

8-42 

10-571948 

60 

i 

413467 

7*84 

984910 

- 5 7 

428557 

8-41 

571443 

5 9 

2 

4 i 3938 

7-83 

984876 

- 5 7 

429062 

8-40 

570938 

58 

3 

414408 

7-83 

984842 

- 5 7 

429666 

8-39 

570434 

57 

4 

414878 

7-82 

984808 

•67 

430070 

8-38 

569930 

56 

5 

4 i 5347 

7-81 

984774 

•67 

430673 

8-38 

569427 

55 

6 

41 58 i 5 

7-80 

984740 

•57 

431075 

8-37 

568926 

54 

7 

416283 

7 - 7 ? 

984706 

•57 

43 1577 

8-36 

568423 

53 

8 

416751 

7-78 

984672 

•57 

432079 

8-35 

567921 

52 

9 

417217 

7'77 

984637 

•67 

43258 o 

8-34 

567420 

5 i 

IO 

417684 

7-76 

984603 

•57 

433 o 8 o 

8-33 

566920 

5 o 

ii 

9 - 4 i 8 i 5 o 

7-75 

9-984569 

•57 

9 - 43358 o 

8-32 

10-666420 

49 

12 

41861 5 

7-74 

984535 

•57 

434 o 8 o 

8-32 

566920 

48 

i 3 

419079 

7-73 

984500 

.57 

434579 

8 - 3 r 

565421 

47 

14 

419644 

7-73 

984466 

•67 

435078 

8 - 3 o 

564922 

46 

i 5 

420007 

7-72 

984432 

• 58 

435576 

8-29 

564424 

45 

16 

420470 

7-71 

984397 

-58 

436073 

8-28 

663927 

44 

*7 

420933 

7-70 

984868 

• 58 

436570 

8-28 

56343 o 

43 

i8 

421395 

7-69 

984328 

• 58 

437067 

8-27 

562933 

42 

19 

421807 

7-68 

984294 

• 58 

43-7563 

8-26 

562437 

41 

20 

4223 i8 

7-67 

984269 

• 58 

438069 

8-25 

561941 

4 o 

21 

9-422778 

7-67 

9-984224 

• 58 

9*438554 

8-24 

io- 56 i 446 

39 

22 

428238 

7-66 

984190 

• 58 

439048 

8-23 

560962 

38 

23 

423697 

7-65 

984135 

• 58 

439543 

8-23 

560467 

37 

24 

424 i 56 

7-64 

984120 

• 58 

44 oo 36 

8-22 

559964 

36 

25 

4246 i 5 

7-63 

984085 

• 58 

440529 

8-21 

559471 

35 

26 

425073 

7-62 

984050 

• 58 

441022 

8-20 

558978 

34 

27 

42553o 

7-61 

984015 

• 58 

44 i 5 i 4 

8-19 

558486 

33 

28 

425987 

7-60 

983981 

• 58 

442006 

8-19 

557994 

32 

29 

426443 

7-60 

983946 

• 58 

442497 

8-18 

55 ~ i 5 o 3 

3 i 

3 o 

426899 

7 - 5 9 

983911 

• 58 

442988 

8-17 

557012 

3 o 

3 i 

9-427354 

7-58 

9-983875 

• 58 

9-443479 

8-16 

io- 55652 i 

20 

32 

427809 

7-5 7 

983840 

• 5 9 

443968 

8-16 

556 o 32 

28 

33 

428263 

7-56 

9 838 o 5 

• 5 9 

444458 

8 • 1 5 

555542 

27 

34 

428717 

7-55 

983770 

• 5 9 

444947 

8-14 

555 o 53 

26 

35 

429170 

7-54 

983780 

• 5 9 

446436 

8* i 3 

554565 

25 

36 

429623 

7-53 

983700 

• 5 9 

445923 

8-12 

554077 

24 

h 

430075 

7-52 

983664 

•69 

446411 

8-12 

553589 

23 

38 

43 o 527 

7-52 

983629 

•69 

446898 

8-11 

553 io 2 

22 

3 9 

430978 

7 - 5 i 

983694 

•69 

447384 

8-io 

5526 i 6 

21 

40 

431429 

7 - 5 o 

983558 

• 5 9 

447870 

8-09 

552 i 3 o 

20 

41 

9-431879 

7-49 

9-98.3523 

• 5 9 

9-448356 

8-09 

io- 55 i 644 

IO 

42 

432329 

7-49 

983487 

•69 

448841 


55 1169 

IO 

43 

432778 

7-48 

933452 

• 5 9 

449326 

0 

8-07 

550674 

17 

44 

433226 

7-47 

98.3416 

- 5 9 

449810 

8-06 

550190 

l6 

45 

433675 

7.46 

98.3381 

•69 

460294 

8* 06 * 

549706 

i 5 

46 

434122 

7-45 

983345 

•69 

430777 

8 -o 5 

549223 

14 

47 

484669 

7-44 

98.3309 

• 5 9 

45i26o 

8 • 04 

jr 548740 

i 3 

48 

435 oi 6 

7-44 

98327.3 

• 60 

45 i 743 

8 -o 3 

548267 

12 

49 

435462 

7-43 

9 332,38 

• 60 

452225 

8-02 

647776 

11 

5 o 

435908 

7-42 

983202 

• 60 

452706 

8-02 

547294 

10 

5 i 

9-436353 

7.41 

9 • 98.3166 

• 60 

9-453187 

8-oi 

io- 5468 i 3 

9 

52 

436798 

7-40 

983i3o 

• 60 

453668 

8 -oo 

546332 

8 

53 

487242 

7 - 4 o 

983094 

• 60 

454148 

7-99 

545852 

7 

54 

487686 

7-89 

983008 

• 60 

454628 

7-99 

645372 

6 

00 

438129 

7-38 

983022 

• 60 

466107 

7-98 

644893 

5 

56 

438572 

7-37 

982986 

• 60 

455586 

7-97 

544414 

4 

57 

439014 

7-36 

982960 

• 60 

466064 

7.96 

543936 

3 

58 

439456 

7-36 

982914 

• 60 

456542 

7-96 

543458 

2 

5 9 

439897 

7-35 

982878 

• 60 

467019 

7 - 9 5 

542981 

1 

60 

44 o 338 

7-34 

982842 

• 60 

467496 

7-94 

542004 

0 


Cosine 

D. 

Sine 


Cotang. 

D. 

Tang. 

M. 


(74 DEGREES.) 








































I 


34 ( 1(3 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

s 

0 

9 - 44 o 338 

7-34 

9-982842 

• 60 

9-457496 

7-94 

10 -542504 

60 

i 

440778 

7-33 

982805 

• 60 

457973 

7- 9 3 

642027 


2 

441218 

7-32 

982769 

• 61 

458449 

7- 9 3 

54 i 55 i 

58 

3 

441 658 

7 * 3 1 

982733 

• 61 

458925 

7.92 

641075 

57 

4 

442096 

7 * 3 1 

982696 

♦ 61 

459400 

7.9 1 

.540600 

56 

5 

442535 

7 - 3 o 

982660 

•61 

459875 

7-90 

640125 

55 

6 

442973 

7-29 

982624 

•61 

460349 

7-90 

539661 

54 

7 

4434 io 

7-28 

982587 

•61 

460823 

7-89 

539177 

53 

8 

443847 

7-27 

982551 

•61 

461297 

7-88 

538703 

52 

9 

444284 

7-27 

982514 

•61 

461770 

7-88 

53823o 

5 i 

IO 

444720 

7-26 

982477 

•61 

462242 

7-87 

537758 

5 o 

11 

9-4401 55 

7-25 

9-982441 

•61 

9-462714 

7*86 

10-537286 

49 

12 

445590 

7-24 

982404 

-6i 

463 186 

7-85 

5368 i 4 

48 

i 3 

446025 

7-23 

982367 

•61 

463658 

7-85 

536342 

47 

i 4 

446459 

7-23 

982331 

•61 

464129 

7-84 

535871 

46 

i 5 

446893 

7-22 

982294 

•61 

464599 

7-83 

5354 oi 

45 

16 

447326 

7-21 

982267 

•61 

465069 

7*83 

53493 i 

44 

17 

447759 

7-20 

982220 

•62 

466589 

7-82 

534461 

43 

10 

448191 

7-20 

982183 

•62 

466008 

7 • 81 

533992 

42 


448623 

7-10 

982146 

•62 

466476 

7-80 

533524 

4 i 

PO 

449054 

7-18 

982109 

•62 

466945 

7-80 

533 o 55 

4 o 

21 

9-449485 

7-17 

9-982072 

•62 

9-467413 

7’79 

10-532587 

3 9 

22 

44991 5 

7-16 

982035 

•62 

467880 

7-78 

532120 

38 

23 

45 o 345 

7 • 16 

981998 

•62 

468347 

7-78 

53 1 653 

37 

24 

450775 

7 -i 5 

981961 

•62 

468814 

I'll 

53 i186 

36 

25 

45 i 2 o 4 

7 • i 4 

981924 

•62 

469280 

7 - 7 6 

530720 

35 

26 

45 i 632 

7 -i 3 

981886 

•62 

469746 

7.75 

53 o 254 

34 

27 

452 o 6 o 

7 * i 3 

981849 

•62 

470211 

7.75 

529789 

33 

28 

452488 

7.12 

981812 

•62 

470676 

7*74 

629324 

32 

29 

452916 

7 -n 

981774 

•62 

471U1 

7-73 

52885 Q 

3 i * 

3 o 

453342 

7-10 

981737 

•62 

471606 

7-73 

528393 

3 o 

3 i 

9-453768 

7-10 

9-981699 

•63 

9-472068 

7-72 

10-527932 

29 

32 

454194 

7’°9 

981662 

•63 

472532 

I ' l 1 

527468 

28 

33 

454619 

7-08 

981625 

•63 

472995 

7-71 

527005 

27 

34 

455 o 44 

7-07 

981587 

•63 

473467 

7-70 

526543 

26 

35 

455469 

7-07 

981549 

•63 

473919 

7-69 

626081 

25 

36 

455893 

7.06 

981512 

•63 

47438 i 

7-69 

5256 iq 

24 

3 7 

4563 16 

7 -o 5 

981474 

•63 

474842 

7-68 

525 i 58 

23 

38 

466739 

7-04 

981436 

•63 

4753 o 3 

7-67 

524697 

22 

39 

457162 

7-04 

981399 

•63 

476763 

7-67 

524237 

21 

4 o 

457584 

7 -o 3 

981361 

•63 

476223 

7-66 

523 777 

20 

41 

9 - 458 oo 6 

7-02 

9-981323 

•63 

9-476683 

7-65 

io- 5233 i 7 

IO 

42 

458427 

7-01 

981285 

•63 

477*42 

7-65 

522858 

IO 

43 

458848 

7-01 

981247 

•63 

477601 

7-64 

522399 

17 

44 

469268 

7-00 

981209 

•63 

478059 

7 - 63 ' 

521941 

l6 

45 

469688 

6-99 

981171 

•63 

478517 

7 • 63 

521483 

i 5 

46 

460108 

6-98 

9811 33 

• 64 

478976 

7-62 

521025 

14 

47 

460527, 

6-98 

981095 

•64 

479432 

7-61 

52 o 568 

i 3 

48 

460946 

6-97 

981057 

•64 

479889 

7-61 

5201 11 

12 

49 

46 i 364 

6-96 

981019 

• 64 

48 o 345 

7-60 

519655 

11 

5 o 

461782 

6-95 

980981 

•64 

480801 

7 - 5 9 

619199 

10 

5 i 

9-462199 

6-95 

9-980942 

• 64 

9-481257 

7-69 

io-518743 

9 

52 

462616 

6-94 

980904 

.64 

481712 

7-58 

518288 

8 

53 

463o32 

6-93 

980866 

•64 

482167 

7.57 

617833 

7 

54 

463448 

6-93 

980827 

• 64 

482621 

7 • 67 

517379 

6 

55 

463864 

6-92 

980789 

• 64 

483075 

7-56 

516926 

5 

56 

464279 

6-91 

980750 

•64 

483529 

7 • 55 

516471 

4 ! 

5 7 

464694 

6-90 

9807i2 

•64 

48398? 

7 • 55 

5 16018 

3 : 

58 

465 108 

6-90 

980673 

• 64 

484435 

7-54 

5 i 5565 

2 

5 g 

465522 

6*89 

980635 

• 64 

484887 

7-53 

5 1 5 11 3 

1 1 

60 

465935 

6-88 

980596 

• 64 

485339 

7-53 

5 i 466 i 

0 i 


Cosine 

E>. 

Sine 


Cotang. 

D. 

Tang. 

M. | 


(73 DEGREES.) 














































SINES AND TANGENTS. (17 DEGREES.) 35 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9-465935 

6-88 

9-980596 

• 64 

9-485339 

7-55 

io- 5 i 466 i 

60 

i 

466348 

6-88 

98o558 

• 64 

485791 

7-52 

514209 

5 q 

2 

466761 

6-87 

980519 

•65 

486242 

7 ' 5 1 

5 i 3 7 58 

58 

3 

467173 

6-86 

980480 * 

•65 

486693 

7 * 5 1 

5 13307 

67 

4 

467685 

6-85 

980442 

•65 

487143 

7 - 5 o 

512857 

56 

5 

467996 

6-85 

980403 

•65 

487693 

7*49 

512407 

55 * 

6 

468407 

6-84 

980364 

•65 

488043 

7-49 

5 i1957 

54 

7 

468817 

6-83 

980325 

•65 

488492 

7-48 

5 i1608 

53 

8 

469227 

6-83 

980286 

•65 

488941 

7-47 

5 11069 

52 

9 

469637 

6-82 

980247 

•65 

489390 

. 7-47 

5 10610 

5 i 

10 

470046 

6-8! 

980206 

• 65 

489833 

7.46 

510162 

5 o 

ii 

9-470455 

6-80 

9-980169 

-65 

9-490286 

7.46 

10-509714 

49 

12 

470863 

6-80 

980130 

• 65 

490733 

7-45 

509267 

48 

i 3 

471271 

6-79 

980091 

-65 

491180 

7-44 

508820 

47 

U 

471679 

6-78 

980002 

-65 

491627 

7-44 

5 o 8373 

46 

i 5 

472086 

6-78 

980012 

-65 

492073 

7-43 

507927 

45 

16 

472492 

6-77 

979973 

-65 

492619 

7-43 

507481 

44 

*7 

472698 

6-76 

979934 

-66 

492965 

7.42 

5 o 7 o 35 

43 

18 

4733 o 4 

6-76 

979895 

-66 

493410 

7.41 

506590 

42 


473710 

6-75 

979855 

-66 

493854 

7.40 

5 o 6 i 46 

4 i 

20 

474 i i 5 

6-74 

979816 

• 66 

494299 

7.40 

506701 

40 

21 

9 - 4745 I 9 

6-74 

9-979776 

-66 

9-494743 

7.40 

io- 5 o 5257 

39 

22 

474923 

6-73 

979737 

• 66 

496186 

7--39 

5 o 48 i 4 

38 

23 

475327 

6-72 

979697 

-66 

49563 o 

I7.38 

604370 

37 

24 

475730 

6-72 

979668 

-66 

496073 

7-37 

503927 

36 

25 

476 i 33 

6-71 

979618 

• 66 

4965 i 5 

7-37 

5 o 3485 

35 

26 

476536 

6-70 

979579 

• 66 

496957 

7-36 

5 o 3 o 43 

34 

27 

476938 

6-69 

979039 

-66 

497399 

7-36 

5 o 26 oi 

33 

28 

477340 

6-69 

979499 

-66 

497841 

7-35 

5 o 2 i 59 

32 

29 

477741 

6-68 

979409 

-66 

498282 

7-34 

501718 

3 i 

3 o 

478142 

6-67 

979420 

-66 

498722 

7-34 

601278 

3 o 

3 i 

9-478642 

6-67 

9-979380 

• 66 

9-499163 

7-33 

io* 5 oo 837 

29 

32 

478942 

6*66 

979340 

• 66 

499603 

7-33 

5 oo 3 o 7 

28 

33 

479342 

6-65 

979300 

.67 

600042 

7-32 

499968 

27 

34 

479741 

6-65 

979260 

• 67 

600481 

7 * 3 * 

499519 

26 

35 

480140 

6-64 

979220 

.67 

500920 

7 - 3 i 

499080 

25 

36 

480539 

6-63 

979180 

.67 

5 oi 359 

7 - 3 o 

498641 

24 

37 

480987 

6-63 

979140 

• 67 

601797 

7 - 3 o 

498203 

23 

38 

48 i 334 

6-62 

979100 

• 67 

5 o 2235 

7.29 

497765 

22 

3 9 

481731 

6 ♦ 61 

979059 

• 67 

602672 

7 • 28 

497328 

21 

4 o 

482128 

6 • 61 

979019 

• 67 

5 o 3 io 9 

7-28 

496891 

20 

4 i 

9-482525 

6-60 

9-978979 

.67 

g- 5 o 3546 

7-27 

10-496454 

10 

42 

482921 

6-59 

978939 

.67 

503982 

7-27 

496018 

l8 

43 

4833 i 6 

6 *59 

978898 

.67 

5 o 44 i 8 

7.26 

495582 

17 

44 

483712 

6-58 

978858 

.67 

5 o 4854 

7-25 

496146 

l6 

45 

484107 

6-5 7 

978817 

.67 

605289 

7-25 

494711 

i 5 

46 

484501 

6-5 7 

978777 

.67 

605724 

7-24 

494276 

i 4 

47 

484895 

6-56 

978736 

• 67 

506169 

7-24 

493841 

i 3 

48 

485289 

6-55 

978696 

• 68 

606598 

7*23 

493407 

12 

49 

485682 

6-55 

978606 

• 68 

507027 

7-22 

492973 

11 

5 o 

48607 5 

6 • 54 

978615 

• 68 

507460 

7-22 

492940 

10 

5 i 

9-486467 

6-53 

9-978574 

• 63 

9*507893 

7-21 

10-492107 

9 

52 

486860 

6-53 

978533 

• 68 

5 o 8326 

7-21 

491674 

8 

53 

487261 

6-52 

978493 

• 68 

608769 

7-20 

491241 

7 

54 

487643 

6 * 5 1 

978402 

• 68 

509191 

7 • 19 

490809 

6 

55 

488034 

6 - 5 1 

978411 

• 68 

609622 

7-19 

490378 

5 

56 

488424 

6 - 5 o 

978370 

• 68 

5 10004 

7-18 

489946 

4 

57 

488814 

6 - 5 o 

978329 

• 68 

5 1 0485 

7-18 

4895 1 5 

3 

58 

489204 

6-49 

978288 

• 68 

610916 

7 * 1 7 

489084 

2 

59 

489693 

6-48 

978247 

• 68 

5 i 1346 

7-16 

488654 

1 

60 

489982 

6-48 

978206 

• 68 

5 i1776 

7-16 

488224 

0 

I Cosine 

D. 

Sine 

D. 

Cotimg. 

D. 

Tang. 

M. 

—- 


17 (72 DEGREES.) 
















































36 (18 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

0 

9-489982 

6-48 

9-978206 

-68 

9-611776 

7-16 

10-488224 

i 

490371 

6-48 

978165 

-68 

512206 

7.16 

487794 

2 

490759 

6-47 

978124 

• 68 

5i2635 

7-13 

487365 

3 

491147 

6-46 

978083 

•69 

* 5i3o64 

7-i4 

486936 

4 

49i535 

6-46 

978042 

•69 

5 i 3493 

7-14 

486507 

5 

491922 

6-45 

978001 

•69 

513921 

7 * i3 

486079 

6 

492308 

6-44 

977960 

•69 

5i4349 

7 * i 3 

485651 

7 

492695 

6-44 

9779*8 

•69 

5 i 4777 

7-12 

485223 

8 

493081 

6-43 

977877 

•69 

5 i 52 o 4 

7-12 

484796 

9 

493466 

6-42 

977835 

• 69 

5 i 5631 

7-u 

484869 

10 

498851 

6-42 

• 977794 

•69 

516067 

7-10 

483943 

11 

9-494236 

6-41 

9-977752 

-69 

9•516484 

7-10 

io- 4835 i 6 

12 

494621 

6-4i 

977711 

•69 

516910 

7-09 

483090 

i3 

496005 

6-40 

977669 

-69 

517335 

7-09 

482665 

14 

495388 

6-39 

977628 

•69 

517761 

7-08 

482239 

i5 

493772 

6-39 

9.77586 

•69 

5i8i85 

7-08 

481816 

16 

496154 

6-38 

977544 

• 70 

5i86io 

7-07 

481390 

n 

496537 

6-3i 

977603 

•70 

519034 

7-06 

480966 

18 

496919 

6-3~j 

97746 i 

.70 

519458 

7-06 

480642 

19 

497301 

6-36 

977419 

• 70 

519882 

7 -o 5 

480118 

20 

497682 

6-36 

977377 

.70 

52o3o5 

7 -o 5 

479696 

21 

9•498064 

6-35 

9-977335 

.70 

9-620728 

7-04 

10-479272 

22 

498444 

6.-34 

977293 

.70 

521151 

7 -o 3 

478849 

23 

498825 

6-34; 

977231 

• 70 

521573 

7 -o 3 

478427 

24 

499204 

6-33 

977209 

.70 

521995 

7 -o 3 

478006 

25 

499684 

6-32 

977167 

• 70 

522417 

7-02 

477583 

26 

499963 

6-32 

977126 

• 70 

522838 

7-02 

477162 

27 

600842 

6-3i 

977083 

•70 

523259 

7-01 

476741 

28 

500721 

6 - 31 

977041 

.70 

52368o 

7-oi 

476820 

29 

501099 

6-3o 

976999 

• 70 

524100 

7-00 

475900 

3o 

501476 

6-29 

976957 

• 70 

524620 

6-99 

476480 

3i 

9-5 oi 854 

6-29 

9-976914 

.70 

9*524939 

6.90 

10-475061 

32 

5 o 223 i 

6.28 

976872 

•7* 

525359 

6.98 

474641 

33 

602607 

6-28 

976880 

.71 

525778 

6.98 

474222 

34 

502984 

6-27 

976787 

•7* 

526197 

6-97 

4738o3 

35 

5o336o 

6-26 

976745 

•7* 

5266 i 5 

6.97 

473385 

36 

5 o 3735 

6-26 

976702 

•7* 

527o33 

6.96 

472967 

37 

5 o 4 i10 

6-25 

976660 

•7i 

527451 

6.96 

472649 

38 

5 o 4485 

6-25 

976617 

•7* 

527868 

6- 9 5 

472i32 

3 9 

5 o 486 o 

6-24 

976574 

•7* 

528286 

6- 9 5 

471715 

40 

5 o 5234 

6-23 

. 976382 

•7* 

528702 

6.94 

471298 

4i 

9-5 o 56 o 8 

6-23 

9-976489 

•7* 

9-529119 

6. 9 3 

10-470881 

42 

506981 

6-22 

976446 

•7* 

529533 

6. 9 3 

470465 

43 

5 o 6354 

6-22 

976404 

•7* 

529960 

6- 9 3 

47oo5o 

44 

506727 

6-21 

976361. 

•7* 

53o366 

6.92 

469634 

45 

507099 

6-20 

676318 

• 71 

530781 

6.91 

469219 

46 

507471 

6-20 

976275 

•7* 

531196 

6.91 

468804 

47 

507843 

6-19 

976232 

• 72 

53i6i1 

6.9° 

46838 o 

48 

5o82i4 

6-19 

976189 

•72 

532025 

6.90 

467976 

49 

5o8585 

6-18 

976146 

•72 

532439 

6.89 

467061 

60 

5 o 8 9 56 

6-18 

976103 

.72 

532853 

6-89 

467147 

5i 

9.509326 

6-17 

9-976060 

•72 

9-533266 

6:88 

10-466734 

52 

509696 

6-16 

976017 

•72 

533679 

6-88 

466821 

53 

5ioo65 

6-16 

975974 

.72 

534092 

6.87 

466908 

54 

5 io 434 

6-i5 

975930 

•72 

5345o4 

6-87 

465496 

55 

5io8o3 

6 -15 

975887 

•72 

534916 

6-86 

465 o 84 

56 

511172 

6-14 

975844 

•72 

535328 

6-86 

464672 

57 

5n54o 

6 -13 

975800 

•72 

535739 

6-85 

464261 

58 

511907 

6-13 

975757 

.72 

536i5o 

6-85 

46385 o 

5 9 

5l22l5 

6-12 

975714 

•72 

53656i 

6-84 

463439 

60 

512642 

6-12 

975670 

•72 

536972 

6-84 

463028 


Cosine 

D. 

Sine 

1 D. 

Cotang. 

D. 

Tang, 


(71 DEGREES.) 


I totoiotototoioiofoto WWOJCjOjWOJOjWW OiOiOiOiOiOiOiyiOiOiO 

o <-> M Ui O'"! OOO o H u WJ>v U> 0-4 GOO O ” W Wfr. Oi 0-4 GOO O H KJ WJX Oi 0~1 COO O >-i to UJ 4^ O O-J QCO O 













































SINES AND TANGENTS. (19 DEGREES.) 


37 


M. 

Sine 

D. 

Cosine 

D. 

J Tang. 

D. 

Cotang. 


o 

9*512642 

6*12 

9*975670 

•73 

9*536972 

6 • 84 

10*463028 

60 

i 

5 13009 

6*ii 

976627 

* 7 3 

53 7 382 

6*83 

462618 

5 9 

2 

5 i 3375 

6*n 

975583 

•73 

537792 

6*83 

462208 

58 

3 

5 13741 

6*io 

975539 

.73 

538202 

6*82 

461798 

67 

4 

514107 

6*09 

976496 

.73 

5386 11 

6*82 

461389 

56 

5 

5 i 4472 

6*09 

. 975462 

• 73 

539020 

6 • 81 

460980 

55 

6 

514867 

6* 08 

976408 

.73 

539429 

6 - 81 

460071 

54 

7 

5 l 5202 

6* 08 

975365 

•73 

689837 

6* 80 

460163 

53 

8 

5 1 5566 

6*07 

975321 

.73 

540245 

6* 80 

469755 

52 

9 

616930 

6*07 

976277 

.73 

54 o 653 

6*79 

.439347 

5 i 

10 

616294 

6* 06 

975233 

.73 

541061 

6*79 

458939 

5 o 

ii 

9 * 5 i 6657 

6 *o 5 

9.975189 

.78 

9*541468 

6*78 

10*458532 

49 

12 

517020 

6 *o 5 

976145 

.73 

541875 

6*78 

458 i 25 

48 

i 3 

517382 

6*04 

975101 

.73 

542281 

6*77 

457719 

47 

14 

517745 

6*04 

975067 

.73 

542688 

6*77 

4573 i 2 

46 

i 5 

518107 

6 *o 3 

976013 

*73 

543094 

6*76 

456906 

45 

16 

518468 

6 *o 3 

974969 

•74 

543499 

6*76 

4565 oi 

44 

*7 

518829 

6*02 

974925 

•74 

643900 

6*75 

466096 

43 

18 

519190 

6*oi 

974880 

•74 

5443 io 

6*75 

455690 

42 

19 

519561 

6*oi 

974836 

•74 

5447 1 5 

6*74 

455285 

4 i 

20 

519911 

6*oo 

974792 

•74 

546119 

6*74 

454881 

4 o 

21 

9*520271 

6*oo 

9-974748 

•74 

9*545524 

6*73 

10*454476 

3 9 

22 

5 20631 

5*99 

974703 

•74 

546928 

6*73 

454072 

38 

23 

520990 

5*99 

974659 

•74 

54633 1 

6*72 

453669 

3 7 

24 

521849 

5*98 

974614 

•74 

646735 

6*72 

453200 

36 

25 

521707 

5 98 

974670 

•74 

547138 

6*71 

462862 

35 

26 

522066 

0.97 

974626 

•74 

547540 

6*71 

452460 

34 

27 

522424 

5*96 

97448 i 

•74 

547943 

6*70 

402057 

33 

28 

522781 

5*96 

974436 

•74 

548345 

6*70 

45 16 55 

32 

29 

523 1 38 

5*90 

974391 

•74 

548747 

6*69 

451 203 

3 i 

3 o 

523495 

5*95 

974347 

•75 

549149 

6*69 

45 o 85 i 

3 o 

3 i 

9*523852 

5*94 

9*974302 

* 7 5 

9 * 54955 o 

6*68 

io* 45 o 45 o 

29 

32 

524208 

5*94 

974257 

.75 

649951 

6*68 

450049 

28 

33 

524564 

5*93 

974212 

•75 

55 o 352 

6*67 

449648 

27 

34 

524920 

6*93 

974167 

•73 

550762 

6*67 

449248 

26 

35 

525275 

5*92 

974122 

•75 

05 i162 

6*66 

448848 

25 

36 

52563 o 

5*91 

974077 

.70 

55 i 552 

6*66 

448448 

24 

37 

520984 

5*91 

974032 

.75 

551962 

6*65 

448048 

23 

38 

026339 

5*90 

973987 

* 7 3 

5 o 235 i 

6*65 

447649 

22 

3 9 

526693 

5*90 

973942 

•75 

552760 

6*65 

447260 

21. 

40 

527046 

5*89 

973897 

* 7 5 

553 149 

6*64 

44685 1 

20 

4 i 

9*627400 

5*89 

9*973862 

• 7 j 

9*553548 

6*64 

10*446452 

IO 

42 

627703 

5-88 

973807 

•75 

553946 

6*63 

446 o 54 

l8 

43 

528 io 5 

5*88 

973761 

•75 

554344 

6*63 

44^656 

I? 

44 

528458 

5*87 

978716 

•76 

554741 

6*62 

445269 

l6 

45 

528810 

6*87 

978671 

• 76 

555 139 

6*62 

444861 

i 5 

46 

529161 

5*86 

973625 

• 76 

555536 

6-61 

444464 

14 

47 

529613 

5*86 

97358 o 

•76 

555933 

6*j6i 

444067 

i 3 

48 

629864 ! 

5*85 

973535 

•76 

556329 

6* 60 

443671 

12 

49 

53o2i5 

5*85 

978489 

• 76 

556726 

6* 60 

443275 

11 

5 o 

53 o 565 

5*84 

973444 

•76 

557121 

6 * 5 9 

442879 

10 

5 i 

9*530916 

5*84 

9*973398 

• 76 

9*557517 

6*59 

10*442433 

0 

52 

53 1 265 

5*83 

973352 

.76 

55791 3 

6 * 5 9 

442087 

8 

53 

53 i 6 i 4 

5*82 

973307 

.76 

5583 o 8 

6*58 

441692 

7 

54 

53 i 9 63 

5*82 

973261 

.76 

508702 

6*58 

441298 

6 

55 

532012 

5 *81 

9732 i 5 

• 76 

5/9097 

6*67 

440903 

5 

56 

532661 

5 • 81 

973169 

.76 

559491 

6*67 

440609 

4 

57 

533009 

5 * 80 

973124 

•76 

55 9 885 

6*56 

440115 

3 

58 

533357 

5 * 80 

973078 

•76 

560279 

6*56 

439721 

2 

59 

533704 

5 ,’ l ) 

973082 

*77 

560673 

6*55 

439827 

1 

60 

534 o 52 

0*78 

972986 

•77 

56 1066 

6*55 

438934 

0 

L 

Corine 1 

D. 

Sine 

D. ! 

Cotang. 

D. 

Tang. 

M. 


(70 DEGREES.) 




































































38 (20 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

- - 

o 

9-534002 

*5.78 

9-972986 

■11 

9- 56 1066 

6-55 

10-438934 

60 

i 

534399 

5-77 

972940 

•11 

56 1409 

6-54 

438541 

5 9 

2 

534745 

5-77 

972894 

■11 

56 1 85 1 

6-54 

438 149 

58 

3 

530092 

5-77 

972848 

•11 

662244 

6-53 

437756 

37 

4 

535438 

5-76 

972802 

•11 

562636 

6-53 

437364 

56 

5 

535783 

5-76 

972755 

■11 

563028 

6-53 

436972 

55 

6 

536129 

5-75 

972709 

•11 

563419 

6-52 

43668 i 

54 

7 

536474 

5-74 

972668 

•11 

I 5638 u 

6-52 

436189 

53 

8 

5368 i 8 

5-74 

972617 

■11 

564202 

6 - 5 i 

435798 

52 

9 

537163 

5- 7 3 

972570 

•11 

664692 

6 - 5 1 

435408 

5 i 

IO 

537507 

5-73 

972524 

•11 

564983 

6 - 5 o 

435017 

5 o 

u 

9-537851 

5-72 

9-972478 

•11 

9-565373 

6 - 5 o 

10-434627 

49 

12 

538 ig 4 

5-72 

97243 i 

.78 

565763 

6-49 

434237 

48 

i 3 

538538 

5-71 

972385 

.78 

566 i 53 

6-49 

433847 

47 

U 

53888 o 

5-71 

972338 

.78 

566542 

6*49 

433458 

46 

i 5 

539223 

. 5-70 

972291 

.78 

566932 

6-48 

433 o 68 

45 

16 

539060 

5-70 

972245 

.78 

567320 

6-48 

432680 

44 

17 

539907 

6-69 

972198 

•78 

567709 

6-47 

432291 

43 

18 

540249 

5-69 

97 21 5 1 

.78 

568098 

6-47 

481902 

42 

19 

540590 

5-68 

972105 

.78 

568486 

6-46 

43 1 5 1 4 

4 i 

20 

540931 

5-68 

972058 

.78 

56887 3 

6-46 

431127 

40 

21 

9-541272 

5-67 

9-972011 

• 78 

9-669261 

6-45 

10-430739 

3 9 

22 

54 i 6 i 3 

5-67 

971964 

• 7 g 

569648 

6-45 

43 o 352 

38 

23 

541953 

5-66 

97 1 9 1 7 

•78 

570035 

6-45 

429965 

37 

24 

542293 

5-66 

971870 

.78 

570422 

6-44 

429678 

36 

25 

542632 

5-65 

971823 

•78 

570809 

6-44 

429191 

35 

26 

542971 

5-65 

97*776 

.78 

571195 

6-43 

428805 

34 

27 

5433 10 

5-64 

971729 

•79 

571 58 i 

6-43 

428419 

33 

28 

543649 

5-64 

971682 

•79 

571967 

6-42 

428o33 

32 

29 

543987 

5-63 

971635 

•79 

572352 

6-42 

427648 

3 i 

3 o 

544325 

5-63 

971588 

•79 

572738 

6-42 

427262 

3 o 

3 i 

9 •544663 

5-62 

9-971540 

•79 

Q• 573 I 23 

6-41 

10-426877 

29 

32 

545 ooo 

5-62 

971493 

•79 

573507 

6-41 

426493 

28 

33 

545338 

5 - 6 i 

971446 

•79 

573892 

6-40 

426108 

27 

34 

545674 

5 - 6 i 

971398 

•79 

574276 

6-40 

426724 

26 

35 

546011 

5 -60 

97 i 35 i 

•79 

574660 

6-39 

425340 

25 

36 

546347 

5 -60 

97i3o3 

*79 

575044 

6-39 

424956 

24 

37 

546683 

5 - 5 9 

971256 

•79 

575427 

6-39 

424573 

23 

38 

547019 

5,59 

971208 

•79 

576810 

6-38 

424190 

22 

3 9 

547354 

5-58 

971161 

•79 

576193 

6-38 

423807 

21 

4 o 

547689 

5-58 

97 Hi 3 

•79 

576676 

6-37 

423424 

20 

4 i 

9-648024 

5-57 

9-971066 

• 80 

9*576953 

6-37 

io- 423 o 4 i 

19 

42 

54830 o 

5*57 

971018 

• 80 

577341 

6-36 

422659 

IS 

43 

548693 

5-56 

970970 

• 80 

577723 

6-36 

422277 

17 

44 

549027 

5-56 

970922 

• 80 

578104 

6-36 

421896 

l6 

45 

549360 

5-55 

970874 

-8o 

578486 

6-35 

42 i 5 i 4 

i 5 

46 

549693 

5-55 

970827 

• 80 

578867 

6-35 

4211 33 

14 

47 

550026 

5-54 

970779 

• 80 

579248 

6-34 

420752 

i 3 

48 

55 o 359 

5-54 

970731 

• 80 

579629 

6-34 

420371 

12 

49 

550692 

5-53 

970683 

• 80 

580009 

6-34 

419991 

11 

5 o 

55 io 24 

5-53 

970635 

• 80 

580389 

6-33 

419611 

10 

5 i 

9• 55 i 356 

5-52 

9-970586 

• 80 

9-580769 

6-33 

10-419281 

Q 

52 

551687 

5-52 

970538 

-8o 

58 i149 

6-32 

4 i$ 85 i 

y 

53 

552 oi 8 

5-52 

970490 

• 80 

58 1 528 

6-32 

418472 

7 

54 

552349 

5 - 5 i 

970442 

• 80 

581907 

6-32 

418093 

6 

55 

55268o 

5 • 51 

970394 

• 80 

582286 

6 • 3 1 

417714 

5 

56 

553 oio 

5 - 5 o 

970340 

•81 

582665 

6 - 3 i 

417335 

4 

57 

553341 

5 - 5 o 

970297 

•81 

583043 

6 - 3 o 

416957 

3 

58 

553670 1 

5.49 

970249 

•81 

583422 

6 - 3 o 

416678 

2 

5 9 

554 ooo 

5-49 

970200 

•81 

5838 oo 

6-29 

416200 

1 

60 

554329 

5-48 

970152 

-81 

584177 

6-29 

4 i 5823 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

-Tang. 

M. 


(69 DEGREES.) 















































SINES AND TANGENTS. (21 DEGREES.) 39 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9-554329 

5-48 

9-970102 

• 81 

9-684177 

6-29 

io- 4 i 5823 

60 

i 

554658 

5-48 

970103 

• 81 

584555 

6-29 

4 i 5445 

59 

2 

554987 

5-47 

970055 

• 81 

584932 

6-28 

4 i 5 o 68 

58 

3 

5553 1 5 

5-47 

970006 

• 81 

585309 

6-28 

4 14691 

57 

4 

555643 

5-46 

969957 

• 81 

585686 

6-27 

4 1 43 1 4 

56 

5 

555971 

5-46 

969909 

• 81 

586062 

6-27 

413938 

55 

6 

556299 

5 -4D 

969860 

• 81 

58643 9 

6-27 

4 i 3 d 6 i 

54 

7 

556626 

5-45 

969811 

•81 

5868 id 

6-26 

41 3 1 85 

53 

8 

556953 

5-44 

969762 

• 81 

587190 

6-26 

412810 

52 

9 

557280 

5-44 

969714 

• 81 

587566 

6-25 

412434 

5 i 

10 

557606 

5-43 

969665 

• 81 

587941 

6-25 

412069 

5 o 

11 

9-567932 

5-43 

9-969616 

.82 

9- 5383 16 

6-25 

10-411684 

4 o 

12 

558258 

5-43 

969667 

• 82 

688691 

6-24 

411309 

48 

i 3 

558583 

5-42 

969518 

•82 

689066 

6-24 

410934 

47 

U 

558909 

5-42 

969469 

-82 

689440 

6-23 

410060 

46 

ID 

55 g 234 

5 - 4 i 

969420 

-82 

589814 

6-23 

410186 

45 

16 

559558 

5 - 4 i 

969370 

-82 

590188 

6-23 

409812 

44 


55 9 8 S 3 

5 - 4 o 

969321 

•82 

590662 

6-22 

409438 

43 

18 

560207 

5 - 4 o 

969272 

•82 

690935 

6-22 

4 ooo 65 

42 

*9 

56 o 53 i 

5.39 

969223 

-82 

691308 

6-22 

408692 

41 

20 

56 o 855 

5 - 3 9 

969173 

• 82 

591681 

6-21 

408319 

40 

21 

9-561178 

5-38 

9-969124 

• 82 

9-592054 

6-21 

10-407946 

3 9 

22 

56 1 5 o1 

5-38 

969076 

• 82 

692426 

6*20 

407574 

38 

23 

561824 

5-37 

969025 

.82 

• 592798 

6-20 

407202 

37 

24 

562146 

5-37 

968976 

• 82 

593170 

6-19 

406829 

36 

2D 

562468 

5-36 

968926 

• 83 

593542 

6-19 

406458 

35 

26 

562790 

5-36 

968877 

• 83 

593914 

6-18 

406086 

34 

27 

563 112 

5-36 

968827 

• 83 

694285 

6-18 

4 o 57 i 5 

33 

28 

563433 

5-35 

968777 

• 83 

594666 

6-18 

405344 

32 

29 

563755 

5 35 

968728 

-83 

596027 

6-17 

404973 

3 i 

3 o 

564075 

5-34 

968678 

-83 

596898 

6-17 

404602 

3 o 

3 i 

9-564396 

5-34 

9-968628 

-83 

9-595768 

6-17 

io* 4 o 4232 

29 

32 

564716 

5-33 

968678 

-83 

596188 

6-16 

4o3862 

28 

33 

565 o 36 

5-33 

968628 

•83 

596508 

’6-16 

403492 

27 

34 

565356 

5-32 

968479 

• 83 

596878 

6-16 

4 o 3 122 

26 

3 d 

566676 

5-32 

968429 

• 83 

597247 

6 -1 5 

402753 

25 

36 

666995 

5 • 3 1 

968379 

.83 

597616 

6-15 

402384 

24 

3 7 

5663 14 

5 - 3 1 

968329 

-83 

59798D 

6 • 1 5 

4 o 2 oi 5 

23 

38 

566632 

5 - 3 1 

968278 

• 83 

5 9 8354 

6* 14 

401646 

22 

3 9 

566951 

5 - 3 o 

968223 

-84 

598722 

6-14 

401278 

21 

4 o 

667269 

5 - 3 o 

968178 

•84 

599091 

6-13 

400909 

20 

4 i 

9-567587 

5-29 

9-968128 

.84 

9-599459 

6 • 1 3 

io- 4 oo 54 i 

19 

42 

567904 

5-29 

968078 

.84 

D99327 

6 -1 3 

400173 

l8 

43 

568222 

5-28 

968027 

.84 

600194 

6-12 

399806 

17 

44 

568539 

5-28 

07977 

.84 

600662 

6-12 

399438 

16 

45 

568856 

5-28 

967927 

.84 

6ooq2q 

6-11 

399071 

i 5 

46 

569172 

5-27 

967876 

.84 

601296 

6-11 

398704 

14 

47 

569488 

5-27 

967826 

.84 

601662 

6-h 

3 9 S 338 

i 3 

48 

569804 

5-26 

967775 

.84 

602029 

6-io 

397971 

12 

i 9 

570120 

5-26 

967725 

.84 

60239O 

6-io 

897606 

11 

5 o 

570435 

5-25 

967674 

• 84 

602761 

6-io 

397239 

10 

5 i 

9-570751 

5-25 

9-967624 

.84 

9- 6 o 3 127 

6-09 

10-396873 

0 

D2 

571066 

5-24 

967673 

.84 

6 o 3493 

6-09 

396507 

8 

53 

671380 

5-24 

967522 

.85 

6 o 3858 

6-09 

396142 

7 

54 

571693 

5-23 

967471 

.85 

604223 

6-08 

3 9' ) 777 

6 

55 

572009 

5-23 

967421 

• 85 

604688 

6-08 

396412 

5 

56 

572323 

5-23 

967370 

• 85 

604953 

6-07 

39D047 

4 

5 7 

572636 

5-22 

967319 

-85 

6 o 53 17 

6-07 

394683 

3 

58 

572950 

5*22 

967268 

• 85 

6 o 5682 

6-07 

3 9 43 18 

2 

5 9 

5 7 3263 

5-21 

967217 

-85 

606046 

6-06 

898964 

1 

60 

673570 

5-21 

967166 

• 85 

606410 

6-06 

898090 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 


M. 


(G8 DEGREES.) 





































40 


(22 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

1 

2 

3 

4 

5 

6 

l 

9 

10 

11 

12 

1 3 

14 

1 5 

16 

n 

18 

*9 

20 

21 

22 

23 

24 

25 

26 

27 

28 

3 ? 

3 1 

32 

33 

34 

35 

36 

37 

38 

3 9 

4 0 

4 1 

42 

43 

44 

45 

46 

47 

48 

g 

5 1 

52 

53 

54 

55 

56 

5 7 

58 

£ 

9-573675 

5 7 3888 

574200 

574512 

574824 

575 i 36 

575447 

5 7 5 7 58 

576069 

576379 

676689 

9*576999 

677809 

677618 

577927 

578236 

678545 

5 7 8853 

579162 

579470 

5 79777 

9 * 58 oo 85 
58 o 392 
580699 
58 ioo 5 
58 1 3 12 
58 1618 
681924 
582229 
58253 d 
582840 

9 * 583 145 
583449 
583754 
584 o 58 
58436 i 
584665 
584968 
585272 
585574 
5858 77 

9 - 586179 
686482 
586783 
587085 
587386 
58 7 688 
587989 
588289 
588590 
5888 9 o 

9*589190 

589489 

589789 

590088 

590387 

590686 

590984 

591282 

5 gi 58 o 

591878 

5*21 

5*20 

5*20 

5 * 19 
5*19 
5*19 

5 * 18 

5 * 18 

5 * 17 
5 *i 7 

5 *16 

5 * 16 

5 * 16 

5 • 1 5 

5 • 1 5 

5 * 14 

5 * 14 

5 • 1 3 

5 • 1 3 

5 * i 3 
5*12 

5*12 

5 *n 

5 *ii 

5 *ii 

5 *io 

5 * 10 
5*09 
5*09 
5*09 
5 *oo 

5 *08 
5*07 
5*07 

5 * 06 
5 *o 6 

5 * 06 
5 *o 5 
5 *o 5 

5 • 04 
5 *o 4 

5 *o 3 

5 *o 3 

5 *o 3 

5*02 

5*02 

5 *oi 

5 *oi 

5 *oi 

5 *oo 

5 *oo 

4*99 

4*99 

4*99 

4*98 

4*98 

4-97 

4-97 

4-97 

4*96 

4.96 

9*967166 

967116 

967064 

967013 

966961 

966910 

966869 

96680.8 

966756 

966706 

966653 

9*966602 

96655 o 

966499 

966447 

966396 

966344 

966292 

966240 

966188 

966136 

9*966085 

966033 

965981- 

965928 

966876 

966824 

966772 

965720 

965668 

966616 

9 *965563 
9655 11 
965458 
965406 
965353 
9653 oi 
965248 
965196 
965143 

966090 

9*965037 

964984 

964931 

964879 

964826 

964773 

964719 

964666 

964613 

964660 

9*964607 

964474 

964400 

964347 

964294 

964240 

964187 

964133 

964080 

964026 

• 85 
*85 

• 85 
*85 
*85 
*85 
*85 
*85 
*86 
*86 
*86 

•86 

*86 

• 86 
*86 

• 86T 
*86 
*86 
*86 
*86 
*86 

.87 

.87 

•87 

•87 

•87 

.87 

•87 

•87 

•87 

•87 

•87 

.87 

•87 

•87 

*88 

*88 

• 88 
*88 
*88 
*88 

*88 
*88 
*88 
*88 
*88 
*88 
• 88 
.89 
*89 

•89 

• 89 

•89 

• 89 
*89 
*89 

• 89 
*89 
*89 
*89 

• 89 

9*606410 

606773 

607167 

607600 

607863 

608225 

6 o 8588 

608960 

609612 

609674 

6 ioo 36 

9*610397 
610769 
611120 
611480 
611841 
612201 
6 i 256 i 
612921 
613281 

61 364 i 

9*614000 
6 i 435 o 
614718 
615077 
6 i 5435 
615793 

6161 5 1 
616509 
616867 
617224 

9*617582 

617939 

618296 

618662 

619008 

619364 

619721 

620076 

620462 

620787 

9*621142 

621497 

621862 

622207 

622561 

622915 

623269 

623626 

623976 

624360 

9*624683 

6 . 25 o 36 

625388 

625741 

626093 

626445 

626797 

627149 

627501 

627852 

6*o6 

6* 06 
6 *o 5 
6 *o 5 
6*04 
6*04 
6*04 
6 *o 3 
6 *o 3 
6 *o 3 
6*02 

6*02 

6*02 

6*oi 

6*oi 

6*oi 

6*oo 

6*oo 

6*oo 

5*99 

5*99 

5*98 

5.98 

5.98 

5.97 

5.97 

5.97 

5.96 

5*96 

5*96 

5* 9 5 

5* 9 5 

5 *95 
5*94 
5*94 
5*94 

5*93 

5* 9 3 

5* 9 3 

5*92 

5.92 

5*92 

5*91 

5*91 

5*90 

5*90 

5*90 

5 -09 
5*89 
5*89 
5*88 

5*88 

5*88 

5*87 

5*87 

5*87 

5*86 

5*86 

5*86 

5*85 

5*85 

10*393590 

393227 

392863 

392500 

392137 

391776 

391412 

391050 

390688 

390326 

389964 

10*389603 

389241 

38888 o 

388520 

388159 

387799 

387439 

387079 

386719 

38635 9 

io* 386 ooo 
385641 
385282 
384923 
384565 
384207 
383849 
383491 
383 1 33 
3S2776 

10*382418 

382061 

381705 

38 i 348 

380992 

38 o 636 

380279 

379924 

379068 

379213 

10*378858 

3785 o 3 

378148 

377793 

377439 

377085 

376731 

376377 

376024 

375670 

10*375317 

374964 

374612 

374259 

373907 

373555 

373203 

372851 

372499 

372148 

60 

5 9 

58 

57 

56 

55 

54 

53 

52 

5 i 

5 o 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

l8 

17 

l6 

i 5 

i 4 

i 3 

12 

11 

10 

7 

6 

5 

4 

3 

2 

1 

0 

• 1 Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(67 DEGREES.) 


















































SINES AND TANGENTS. (23 DEGREES.) 41 


M. j 

Sine 

D. 

Cosine | 

D. 

Tang. 

D. 

Cotang. 


0 

9.691878 

4.96 

9-964026 

'o 9 i 

9.627862 

5-85 

10*372148 

60 

i 

592176 1 

4-90 

963972 

•89 

628203 

5-85 

371797 

5 9 

2 

692473 

4-96 

963919 

.89 

628554 

5-85 

371446 

58 

3 

592770 

4-96 

9 63865 

.90 

628905 

5-84 

371095 

57 

4 

693067 

4-94 

963811 

.90 

629255 

5-84 

370745 

56 

5 

5 Q 3363 

4-94 

963757 

.90 

629606 

5-83 

370394 

55 

6 

593669 

4-93 

963704 

.90 1 

629956 

5-83 

370044 

54 

7 

598955 

4-93 

96365o 

.90 

63 o 3 o 6 

5-83 

369694 

53 

8 

694251 

4.93 

963696 

.90 

63 o 656 

5-83 

369344 

52 

9 

594547 

4-92 

963542 

.90 

63 iop 5 

5-82 . 

868996 

5 i 

10 

5^4842 

4-92 

963488 

.90 

63 1 355 

5.82 

368645 

5 o 

1 1 

9.595137 

4-91 

9.963434 

.90 

9-631704 

5.82 

10*368296 

49 

12 

595432 

4-91 

963379 

.90 

632 o 53 

5-81 

367947 

48 

i 3 

596727 

4-91 

963320 

.90 

632401 

5 • 81 

367099 

47 

14 

596021 

4-90 

963271 

.90 

632760 

5 -81 

367200 

46 

i 5 

§9631 5 

4-90 

963217 

.90 

633098 

5-80 

366902 

45 

16 

596609 

4-89 

963 i 63 

. - 9 ° 

633447 

5* 80 

366053 

44 

*7 

596908 

4 - 8 9 

9 & 3 io 8 

• 9 1 

633795 

5* 80 

3662 o 5 

43 

18 

597196 

4.89 

963 o 54 

.91 

634143 

5-79 

360807 

42 

l 9 

597490 

4-88 

962999 

• 9 1 

634490 

5-79 

3655 io 

4 i 

20 

597783 

4-88 

962946 

.91 

634838 

5-79 

365 i 62 

40 

21 

9.598075 

4-87 

9.962890 

• 9 i 

9 - 635 1 85 

5-78 

io. 3648 i 5 

39 

22 

598368 

4-87 

962836 

.91 

635532 

5-78 

364468 

38 

23 

598660 

4-87 

962781 

.91 

635879 

5-78 

364121 

37 

24 

598962 

4-86 

962727 

.91 

636226 

5-77 

363774 

36 

25 

599244 

4-86 

962672 

.91 

636672 

5-77 

363428 

35 

26 

599536 

4-85 

962617 

.91 

636919 

5-77 

363 o 8 i 

34 

27 

599827 

4-85 

962562 

.91 

637260 

5-77 

362735 

33 

28 

600118 

4-85 

962508 

.91 

637611 

5-78 

362389 

32 

29 

600409 

4.84 

962453 

.91 

637 g 56 

5-76 

362044 

3 i 

3 o 

600700 

4.84 

962398 

.92 

638302 

5 * 76 

361698 

3 o 

3 i 

9•600990 

4*84 

9.962343 

.92 

9-638647 

5*75 

io- 36 i 353 

29 

32 

601280 

4-83 

962288 

.92 

638992 

5*75 

361008 

28 

33 

601670 

4-83 

962233 

.92 

639337 

5-75 

36 o 663 

27 

34 

601860 

4-82 

962178 

.92 

639682 

5-74 

36 o 3 i 8 

26 

35 

6021 5 o 

4-82 

962123 

.92 

640027 

5-74 

359973 

25 

36 

602439 

4-82 

962067 

.92 

640371 

5-74 

359629 

24 

3 7 

602728 

4 - 8 i 

962012 

.92 

640716 

5.73 

359284 

23 

38 

603017 

4*8i 

961957 

.92 

641060 

5.73 

358940 

22 

3 9 

6 o 33 o 5 

4 -81 

961002 

.92 

641404 

5-73 

358096 

21 

40 

603594 

4*80 

961846 

.92 

641747 

5*72 

358253 

20 

4 i 

9. 6 o 3882 

4 -80 

9 , 9 6i 79 i 

.92 

9-642091 

5.72 

10.357909 

19 

42 

604170 

4-79 

961735 

.92 

642434 

5.72 

357566 

l8 

43 

604457 

4-79 

961680 

.92 

642777 

5-72 

357223 

H 

44 

6 o 4745 

4-79 

961624 

•93 

643120 

5.71 

35688 o 

l6 

45 

6 o 5 o 32 

4-78 

961669 

• 9 3 

648468 

5-71 

356537 

i 5 

46 

6 o 53 i 9 

4-78 

961 5 i 3 

*93 

6438 o 6 

5-71 

356194 

14 

47 

6 o 56 o 6 

4-78 

961408 

•93 

644148 

5-70 

355852 

i 3 

48 

606892 

4-77 

961402 

• 93 

644490 

5.70 

3555 io 

12 

49 

606179 

4-77 

961346 

• 9 3 

644832 

5.70 

355 68 

11 

5 o 

606465 

4-76 

961290 

• 9 3 

646174 

5*69 

354826 

10 

5 i 

9-606751 

4-76 

9-961235 

• 9 ? 

9 . 6455 i 6 

5.69 

10-354484 

9 

52 

607036 

4-76 

961179 

•93 

645857 

5-69 

354143 

8 

53 

607322 

4-73 

961123 

• 9 3 

646199 

5*69 

3538 oi 

7 

54 

607607 

4-75 

961067 

• 9 3 

646540 

5 -6§ 

35346 o 

6 

55 

607892 

4-74 

961011 

• 9 3 

646881 

5-68 

353 ii 9 

5 

56 

608177 

4-74 

960955 

• 9 3 

647222 

5-68 

352778 

4 

5 7 

608461 

4-74 

960899 

.93 

647562 

5-67 

352438 

3 

58 

608745 

4 - 7 3 

960843 

•94 

647903 

5-67 

352097 

2 

09 

609029 

4-73 

960786 

•94 

648243 

5-67 

301757 

1 

60 

60931 3 

4*73 

960730 

.94 

648583 

5-66 

35 i 4 i 7 

0 


1 Cosine 

1 D. ’ 

Sine 

D. 

! Cotang. 

1 D. 

i Tang. 

M. 


(66 DEGREES.) 


























































42 


(24 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. | 

Tang. 

D. 

Cotang. 


0 

9-609313 

4-78 

9-960730 

•94 

9-648583 

5-66 

io- 35 i 417 

60 

i 

609097 

4-72 

960674 

•94 

648923 

5-66 

351077 

5 9 

2 

609880 

4-72 

960618 

.94 

649263 

5-66 

360737 

58 

3 

610164 

4-72 

960061 

•94 

649602 

5-66 

350398 

57 

4 

610447 

4-71 

960305 

•94 

649942 

5-65 

35 oo 58 

56 

5 

610729 

4-71 

960448 

•94 

65 o 28 i 

5-65 

3497'9 

DO 

6 

611012 

4-70 

960392 

•94 

65 o 62 o 

5-65 

34938 o 

54 

7 

611294 

4-70 

96o335 

•94 

650969 

5-64 

349041 

53 

8 

611676 

4-70 

960279 

.94 

65 1 297 

5-64 

348703 

52 

9 

611 858 

4-69 

960222 

•94 

65 1 636 

5-64 

548864 

5 i 

10 

612140 

4-69 

960166 

•94 

631974 

5-63 

348026 

5 o 

11 

9-612421 

4-69 

9-960109 

- 9 5 

g- 6523 i 2 

5-63 

10-347688 

49 

12 

612702 

4-68 

960032 

-93 

65265 o 

5-63 

34735 o 

48 

i 3 

612983 

4-68 

959995 

-93 

662988 

5-63 

347012 

47 - 

i 4 

613264 

4-67 

959938 

• 93 

653326 

5-62 

346674 

46 

i 5 

6 i 3545 

4-67 

959882 

-93 

653663 

5-62 

346337 

45 

16 

61 3825 

4-67 

959825 

- 9 5 

654 ooo 

5-62 

346000 

44 

*7 

6 i 4 io 5 

4-66 

959768 

- 9 5 - 

654337 

5 - 61 

345663 

43 

18 

61 4385 

4-66 

969711 

-93 

654674 

5 - 6 i 

345326 

42 

19 

614665 

4-66 

959654 

- 9 5 

655 oi1 

5 - 6 i 

344989 

41 

20 

614944 

4-65 

959596 

- 9 5 

655348 

5 • 61 

344652 

40 

21 

g- 6 i 5223 

4-65 

g-g 5 o 539 

- 9 5 

9-655684 

5 -60 

10- 3443 16 

39 

22 

6 i 55 o 2 

4-65 

959482 

- 9 5 

656 o 2 o 

5 -60 

343980 

38 

23 

616781 

4-64 

959426 

-93 

656356 

5 -60 

343644 

37 

24 

616060 

4-64 

959668 

- 9 5 

656692 

5-59 

3433 o 8 

36 

23 

61 6338 

4-64 

959310 

.96 

657028 

3-59 

342972 

35 

26 

616616 

4-63 

959253 

.96 

657364 

5-59 

342636 

34 

27 

616894 

4-63 

959196 

.96 

657699 

6-69 

3423 oi 

33 

28 

617172 

4-62 

g 5 g1 38 

.96 

658 o 34 

5-58 

341966 

32 

29 

617430 

4-62 

959081 

.96 

658369 

5-58 

34 i 63 1 

3 i 

3o 

617727 

4-62 

959023 

•96 

658704 

5-58 

341296 

3o 

3i 

9-618004 

4 -6 i 

9-958965 

• 96 

9-659039 

5-58 

10-340961 

29 

32 

618281 

4 -6 i 

958908 

.96 

669373 

5-57 

340627 

28 

33 

61 8558 

4 -6 i 

95885 o 

.96 

659708 

5-57 

340292 

27 

34 

6 i 8834 

4-60 

958792 

• 96 

660042 

5-57 

339958 

26 

35 

619110 

4-60 

958734 

•96 

660376 

5.57 

339624 

25 

36 

619386 

4-60 

958677 

• 96 

660710 

5-56 

339290 

24 

37 

619662 

4 - 5 9 

968619 

.96 

661o 43 

5-56 

338907 

23 

38 

619938 

4-59 

95856 i 

.96 

661377 

5-56 

338623 

22 

3 9 

620213 

4-69 

9585 o 3 

•97 

661710 

5-55 

338290 

21 

40 

620488 

4-58 

958445 

•97 

662043 

5-55 

337967 

20 

4 i 

9-620763 

4-58 

9-958387 

•97 

9-662376 

5-55 

10-337624 

1 0 

42 

621038 

4-57 

958329 

•97 

662709 

5-54 

337291 

10 

43 

621 3 1 3 

4-57 

968271 

•97 

663 o 42 

5-54 

336 9 58 

17 

44 

621687 

4-07 

968213 

•97 

663375 

5-54 

336625 

l6 

45 

621861 

4-56 

968154 

•97 

663707 

5-54 

336298 

i 5 

46 

622135 

4-56 

958 og 6 

•97 

664039 

5-53 

335961 

14 

47 

622409 

4 • 56 

958 o 38 

•97 

664371 

5-53 

335629 

i 3 

48 

622682 

4-55 

957979 

•97 

664703 

5-53 

335297 

12 

49 

622956 

4-55 

937921 

•97 

665 o 35 

5-53 

334965 

11 

5o 

623229 

4-55 

967863 

•97 

663366 

5-52 

334634 

10 

5 i 

9*6235o2 

4-54 

9-957804 

*97 

9-666697 

5-52 

io- 3343 o 3 

9 

52 

623774 

4-54 

967746 

.98 

666029 

5-52 

333971 

8 

53 

624047 

4-54 

967687 

-98 

66636 o 

5 • 5 1 

333640 

7 

54 

624319 

4-53 

967628 

.98 

66669 1 

5 - 51 

333309 

6 

55 

624391 

4-53 

967670 

-98 

667021 

5 • 51 

332979 

5 

56 

624863 

4-53 

967511 

.98 

667352 

5 - 5 1 

332648 

4 

37 

625 1 35 

4-52 

957462 

.98 

667682 

5 - 5 o 

3323 18 

3 

58 

623406 

4-52 

967393 

•98 

66801 3 

5 - 5 o 

331987 

2 

5 9 

626677 

4-32 

937335 

.98 

668343 

5 - 5 o 

33 1667 

1 

60 

620948 

401 

957276 

.98 

668672 

5-5o 

33 1 328 

0 


Cosine 

D. 

1 Sine, 

D. 

Cotang. 

D. 

1 Tang. 

M. 


(65 DEGREES.) 





































SINES AND TANGENTS. (25 DEGREES.) 


43 


M. 

Si no 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

- - ^ 

0 

9-625948 

4 - 5 i 

9-957276 

.98 

9-668673 

5 - 5 o 

10• 33 1327 

60 

i 

626219 

4 • 5 1 

977217 

•98 

669002 

5-49 

330998 

5 9 

2 

626490 

4 - 5 i 

9671 58 

•98 

669332 

5-49 

33 o 668 

.58 

3 

626760 

4- 5 o 

977099 

.98 

669661 

5-49 

33 o 33 g 

'57 

4 

627030 

4 - 5 o 

967040 

.98 

669991 

5-48 

330009 

56 

5 

627300 

4 - 5 o 

976981 

•98 

670320 

5-48 

329680 

55 

6 

627670 

4-49 

976921 

•99 

670649 

5-48 

32 g 35 i 

54 

7 

627840 

4-49 

966862 

•99 

670977 

5-48 

329023 

53 

8 

628109 

4-49 

976803 

•99 

671306 

5-47 

328694 

52 

9 

628378 

4-48 

966744 

•99 

671634 

5-47 

328366 

5 i 

10 

628647 

4-48 

956684 

•99 

67:963 

5-47 

328037 

5 o 

11 

9-6j§9i6 

4-47 

9-966625 

•99 

9-672291 

5-47 

10-327709 

49 

12 

629185 

4-47 

966666 

•99 

672619 

5-46 

3 2 7 3 S1 

48 

i 3 

629453 

4-47 

9765 o 6 

•99 

672947 

5-46 

327003 

47 

14 

629721 

4-46 

966447 

•99 

673274 

5-46 

326726 

46 

i 5 

629989 

4-46 

966387 

•99 

673602 

5-46 

326398 

45 

16 

630267 

4-46 

966327 

•99 

673929 

5-45 

326071 

44 

n 

63 o 524 

4.46 

966268 

•99 

674257 

5-45 

326743 

43 

18 

630792 

4-45 

966208 

I -00 

674584 

5-40 

3254 i 6 

42 

19 

631069 

4-43 

966148 

1 -00 

674910 

5-44 

326090 

4 i 

20 

63 1 3 26 

4-45 

976089 

I -00 

6772^7 

5-44 

324763 

4 o 

21 

9• 63 1 5 g 3 

4-44 

9-966029 

I -00 

9-675064 

5-44 

io -324436 

39 

22 

63 1869 

4-44 

966969 

I -00 

675890 

5 ■ 44 

324110 

38 

23 

632120 

4-44 

955909 

I -00 

676216 

5-43 

323784 

37 

24 

632392 

4-43 

957849 

I -00 

676543 

5-43 

323467 

36 

25 

632658 

4-43 

966789 

I -00 

676869 

5-43 

3 2 3 1 3 1 

35 

26 

632923 

4-43 

955729 

I -00 

677194 

5-43 

322806 

34 

27 

633189 

4-42 

977669 

I -00 

677620 

5-42 

322480 

33 

28 

633454 

4-42 

955609 

I -00 

677846 

5-42 

322164 

32 

o 9 

633719 

4-42 

955548 

1 -00 

678171 

5-42 

321829 

3 i 

3 o 

633984 

4 - 4 i 

955488 

1-00 

678496 

5-42 

32 i 5 o 4 

3 o 

3 i 

9-634249 

4 - 4 i 

9-955428 

I -01 

9 - 678821 

5 • 41 

10-321179. 

29 

32 

6345 i 4 

4 - 4 o 

955368 

I -01 

679146 

5 - 4 i 

320804 

28 

33 

634778 

4.40 

955307 

I -01 

679471 

5 • 41 

320629 

27 

34 

635o42 

4 - 4 o 

955247 

1 -01 

679795 

5-41 

320205 

26 

35 

6353 o 6 

4-39 

965186 

I -01 

680120 

5 - 4 o 

319880 

25 

36 

635570 

4-39 

955 i 26 

I -01 

680444 

5 - 4 o 

3 ig 556 

24 

37 

635834 


955 o 65 

I -01 

680768 

5 - 4 o 

319232 

23 

38 

636097 

4-38 

955 oo 5 

I -01 

681092 

5 - 4 o 

3 18908 

22 

3 9 

636360 

4-38 

974944 

I -01 

681416 

5 - 3 9 

3 1 8584 

21 

40 

636623 

4-38 

954883 

I -01 

681740 

5 - 3 9 

318260 

20 

4 i 

9-636886 

4-37 

9-954823 

I -01 

9-682063 

5 - 3 9 

10-317937 

19 

42 

637148 

4-37 

954762 

I -01 

682387 

5 - 3 9 

317613 

l8 

43 

637411 

4-37 

954701 

I -01 

682710 

5-38 

317290 

17 

44 

637678 

4-37 

964640 

I -01 

683 o 33 

5-38 

3 16967 

l6 

45 

637935 

4-36 

954679 

I -01 

683356 

5-38 

316644 

i 5 

46 

638197 

4-36 

954518 

I -02 

683679 

5-38 

3 1 63 21 

14 

47 

638458 

4-36 

964457 

I -02 

684001 

5-37 

3 16999 

i 3 

48 

638720 

4-35 

954396 

I -02 

684324 

5-37 

3 i 5676 

12 

49 

638 9 8 i 

4-35 

954335 

I -02* 

684646 

5-37 

3 1 5354 

11 

5 o 

639242 

4-35 

954274 

1-02 

684968 

5-37 

3 i 5 o 32 

10 

5 i 

9 - 6395 o 3 

4-34 

9-964213 

1-02 

9-685290 

5-36 

io- 3 14710 

9 

52 

639764 

4-34 

964162 

I -02 

6856 i 2 

5-36 

314388 

8 

53 

640024 

4-34 

964090 

1-02 

685 g 34 

5-36 

3 14066 

7 

54 

640284 

4-33 

964029 

I -02 

686255 

5-36 

3 13746 

6 

55 

640644 

4-33 

953968. 

I -02 

6865 77 

5-35 

3 1 3423 

5 

56 

640804 

4-33 

953906 

I -02 

68689S 

5-35 

3 1 3 10 2 

4 

57 

641064 

4-32 

953845 

I -02 

687219 

5-35 

312781 

3 

58 

641324 

4-32 

973783 

I -02 

687540 

5-35 

312460 

2 

5 g 

641684 

4-32 

973722 

1 -o 3 

687861 

5-34 

3 121 3 g 

1 

60 

641842 

4 - 3 i 

95366 o 

I -o 3 

688182 

5-34 

3 11818 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(64 DEGREES.) 









































44 (26 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-641842 

4 - 3 i 

9-953660 

1 -o 3 

9-688182 

5-34 

io- 3 i1818 

60 

i 

642101 

4 - 3 1 

953699 

1 -o 3 

6885 o 2 

5-34 

3 11498 

59 

2 

642360 

4 - 3 i 

953537 

1 -o 3 

688823 

5-34 

311177 

58 

57 

3 

642618 

4 - 3 o 

953475 

1 -o 3 

689143 

5-33 

310867 

4 

642877 

4 - 3 o 

9534 i 3 

1 -o 3 

689463 

5-33 

3 10537 

56 

5 

6431 35 

4 - 3 o 

953352 

1 -o 3 

689783 

5-33 

310217 

55 

6 

6433 o 3 

4 - 3 o 

953290 

1 -o 3 

690103 

5 - 3 * 

309897 

54 

7 

64365 o 

4-29 

953228 

1 -o 3 

690423 

5-33 

309577 

53 

8 

643908 

4-29 

953166 

1 -o 3 

690742 

5-32 

309288 

52 

9 

644 i 65 

4-29 

953 io 4 

1 -o 3 

691062 

5-32 

308938 

5 i 

IO 

644423 

4-28 

953042 

1 -o 3 

691381 

5-32 

308619 

5 o 

n 

9•644680 

4-28 

9-962980 

1 -04 

9-691700 

5 • 3 1 

io- 3 #£ 3 oo 

49 

12 

i 3 

644936 

646193 

4-28 

4-27 

952918 

962855 

1 -04 

1 -04 

692019 

692338 

5 • 3 1 

5 - 3 1 

307981 

307662 

48 

47 

14 

645400 

4-27 

952793 

1 • 04 

692666 

5 • 3 1 

307344 

46 

i 5 

645706 

4-27 

952781 

1 • 04 

692976 

5 • 3 1 

307028 

45 

16 

646962 

4-26 

952669 

1 -04 

693293 

5 - 3 o 

306707 

44 

17 

646218 

4-26 

952606 

1 -04 

693612 

5 - 3 o 

3 o 6888 

43 

18 

646474 

4-26 

962544 

1 • 04 

693930 

5 - 3 o 

306070 

42 

19 

646729 

4-25 

952481 

1 • 04 

694248 

5 - 3 o 

305762 

4 i 

20 

646984 

4-25 

952419 

1 -04 

694666 

5-29 

3 o 5434 

4 o 

21 

9-647240 

4-25 

9*952356 

1 -04 

9-694883 

5-29 

io- 3 o 5 i17 

3 9 

22 

647494 

4-24 

952294 

1 -o 4 

695201 

5-29 

304799 

38 

23 

647749 

4-24 

95223 i 

1 -o 4 

695518 

5-29 

304482 

37 

24 

648004 

4-24 

952168 

1 -o 5 

6 q 5836 

5-29 

304164 

36 

25 

648268 

4-24 

952106 

1 -o 5 

696153 

5-28 

3 o 3847 

35 

26 

648612 

4 - 23 

952043 

1 -o 5 

696470 

5-28 

3 o 353 o 

34 

2 7 

648766 

4- 23 

951980 

1 -o 5 

696787 

5-28 

3 o 32 i 3 

33 

28 

649020 

4-23 

951917 

1 -o 5 

697108 

5-28 

302897 

3 o 258 o 

32 

2 9 

649274 

4-22 

951 854 

1 -o 5 

697420 

5-27 

3 i 

3 o 

649527 

4-22 

9 5l 79 r 

1 -o 5 

697736 

6-27 

302264 

3 o 

3 i 

9-649781 

4-22 

9-951728 

1 -o 5 

9-698053 

5-27 

10.301947 

29 

32 

65 oo 34 

4-22 

95 i 665 

1 -o 5 

698369 

6-27 

3 oi 63 i 

28 

33 

660287 

4-21 

951602 

1 -o 5 

698680 

5-26 

3 o1 3 1 5 

27 

34 

65 o 539 

4-21 

961539 

1 -o 5 

699001 

5-26 

300999 

26 

35 

650792 

4-21 

951476 

1 -o 5 

699316 

5-26 

300684 

25 

36 

65 1044 

4-20 

961412 

1 -o 5 

699632 

5-26 

3 oo 368 

24 

37 

65 1297 

4-20 

961349 

1 -06 

699947 

5-26 

3 ooo 53 

23 

38 

65 1 549 

4-20 

951286 

1 -06 

700263 

5-25 

299737 

22 

3 9 

65 1800 

4 -19 

961222 

1 -06 

700678 

5-25 

299422 

21 

4 o 

652 o 52 

4-19 

951159 

1 -06 

700893 

5-25 

299107 

20 

4 i 

9 - 6523 o 4 

4 • 1 9 

9-951096 

1 -06 

9-701208 

5 • 24 

10-298792 

I9 

42 

652555 

4*18 

951082 

1 -06 

7 oi 523 

5-24 

298477 

10 

43 

662806 

4-18 

950968 

1 -06 

701837 

5-24 

298168 

17 

44 

653 o 57 

4-18 

950905 

1 -06 

702152 

5-24 

297848 

l6 

45 

6533 o 8 

4 -18 

950841 

1 -06 

702466 

5-24 

297534 

i 5 

46 

653558 

4-17 

950778 

1 -06 

702780 

5-23 

297220 

14 

47 

6538 o 8 

4-17 

960714 

1 -06 

703096 

5-23 

296905 

i 3 

48 

654059 

4 -i 7 

95 o 65 o 

1 -06 

703409 

5-23 

296391 

12 

49 

654309 

4-16 

960686 

i 1 - 06 

703728 

5-23 

296277 

11 

5 o 

654558 

4-16 

95 o 522 

1-07 

704036 

5-22 

296964 

10 

5 i 

9 - 6548 o 8 

4-16 

9 - 95 o 458 

1 -67 

9 - 7 o 435 o 

5-22 

io- 29565 o 

0 

52 

655 o 58 

4-16 

950394 

95 o 33 o 

1-07 

704663 

5-22 

295337 

8 

53 

655307 

4 • 1 5 

1-07 

704977 

5-22 

295028 

7 

54 

655556 

4 * 1 5 

950266 

l ’ 0 ~l 

705290 

5-22 

294710 

6 

55 

6558 o 5 

4 * 1 5 

950202 

1 -07 

7 o 56 o 3 

5-21 

294397 

5 

56 

656 o 54 

4 -i 4 

95 oi 38 

1-07 

705916 

5-21 

294084 

4 

57 

656302 

4 -i 4 

950074 

1 -07 

706228 

5-21 

293772 

3 

58 

65655 i 

4-14 

950010 

1 -07 

706541 

5-21 

298459 

2 

5 9 

656799 

4-13 

949945 

949881 

1 -07 

706864 

5-21 

2 g 3 i 46 

1 

60 

657047 

4-13 

1 -07 

707166 

5-20 

292834 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(63 DEGREES.) 
















































SINES AND TANGENTS. (27 DEGREES.) 


45 


M. 


o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 
12 

1 3 

1 4 

1 5 

16 

n 

18 

r 9 

20 

21 

22 

23 

24 

25 

26 

27 

28 

8 

3 1 

32 

33 

34 

35 

36 

37 

38 

3 9 

4 0 

4 1 

42 

43 

44 

45 

46 

47 

48 

t 

5 1 

52 

53 

54 

55 

56 

5 7 

58 

8 


Sine 


9-667047 
667296 
667642 
657790 
658 o 37 
668284 
65853 1 
658778 
669025 
659271 
669617 

9-659763 

660009 

660265 

66 o 5 oi 

660746 

660991 

661286 

661481 

661726 

661970 

9-662214 

662459 

662703 

662946 

663190 

663433 

663677 

663920 

664163 

664406 

9•664648 
664891 
665 1 33 
665375 

665617 

665869 

666100 

666342 

666583 

666824 

9-667066 

667306 

667546 

667786 

668027 

668267 

6685 o 6 

668746 

66S986 

669225 

9•669464 
669703 
669942 
670181 
670419 
670658 
670896 

671184 

671372 

671609 


Cosine 


D. 

Cosine 

D. 

4-13 

9-949881 

1-07 

4 -i 3 

949816 

1 -07 

4 ’ 12 

949762 

1 -07 

4 -12 

949688 

1 -08 

4-12 

949623 

i-oS 

4 ’ 12 

949058 

1 -08 

4 -11 

949494 

1 -08 

4 ‘ 11 

949429 

1 -08 

4 -11 

949364 

i-08 

4 -io 

949300 

1 -08 

4 -10 

949235 

1 -08 

4 * 10 

9 - 949 H 0 

i-08 

4 ‘ 09 

949105 

1 -08 

4-09 

4 -o 9 

946040 

948976 

1 -08 

1 -08 

4-09 

948910 

1 -08 

• 4 -o 8 

948845 

1 -08 

4 *o 8 

948780 

1 -09 

4 -08 

948715 

1 -09 

4-07 

948650 

1-09 

4-07 

948584 

1 -09 

4-07 

9-948619 

1 -09 

4-07 

948454 

1-09 

4 -06 

948388 

1-09 

4 ’o 6 

948323 

1 -09 

4 -o 6 

948257 

1 -09 

4 *o 5 

948192 

1-09 

4 -o 5 

948126 

1-09 

4 -o 5 

948060 

1 -09 

4 -o 5 

947995 

1 • 10 

4 -o 4 

947929 

1 • 10 

4 -o 4 

9-947863 

1 • 10 

4 * 04 

947797 

1 • 10 

4 'o 3 

947731 

1 • 10 

4 *o 3 

947665 

1 • 10 

4 -o 3 

947600 

1 • 10 

4‘02 

947533 

1 • 10 

4-02 

947467 

1 • 10 

4 ’02 

947401 

1 • 10 

4-02 

947335 

1 • 10 

4 -oi 

947269 

1 • 10 

4 *oi 

9-947203 

1 • 10 

4 -oi 

947136 

1 • 11 

4 -oi 

947070 

1 • 11 

4 -oo 

947004 

1 • 11 

6 d 

0 0 

946937 

946871 

1 • 11 

1 • 11 

3 ‘99 

946804 

1 • 11 

3-99 

946738 

1 • 11 

3-99 

946671 

1 • 11 

3-99 

946604 

1 • 11 

3 ’ 9 8 

9-946538 


3 ’ 9 8 

946471 

1 • 11 

3- 9 8 

946404 

1 • 11 

3*97 

946337 

1 • 11 

3-97 

946270 

1 • 12 

3-97 

946203 

1 • 12 

A97 

946136 

1 • 12 

3- 9 6 

946069 

1 • 12 

3- 9 6 

946002 

1 • 12 

3-96 

940935 

1 • 12 

D. 

Sine 

D. 


Tang. 


9-707166 

707478 

707790 

708102 

708414 

708726 

709037 

709349 

709660 
70997 1 
710282 

9-710093 

710904 

711215 

7 ii 525 

711836 
712146 
7 r 2466 
712766 
713076 
7 i 3386 

9-713696 

714005 

714314 

714624 
714933 
716242 
71 555 i 
7 i 586 o 
716168 

7 1 6477 

9-716785 
7 1 7 ° 93 , 
717401 

7 1 77°9 

718017 

718325 

7 i 8633 

718940 

719248 

719555 

9-719862 
720169 
720476 
720783 
721089 
721396 
721702 
722009 
7223i 5 
722621 

9-722927 
723232 
723538 

723844 
724149 
724404 
724739 
725 o 65 
725369 
725674 


Cotang. 


D. 


5-20 
5-20 
5-20 
5-20 
5-19 
5*19 
5-19 
5-19 
5-i 
5-i 
5-i8 

5-i8 
5-i8 
5-18 
5-17 
5-17 
5-1? 
5-17 
5-16 
5-i6 
5-16 

5-16 
5-16 
5-10 
5 • 1 5 
5 • 15 
5 • 1 5 
5-14 
5-i4 
5-14 
5-i4 

5-i4 
5-13 
5-13 
5-13 
5-13 
5 -13 
5-12 
5-12 
5-12 
5-12 

5-12 
5 -ii 
5-11 
5-11 
5-11 
5-11 
5-io 
5-io 
5-io 
5-io 

5-io 

5-09 

5-09 

5-09 

5-09 

5-09 

5-08 

5-08 

5 -o 8 i 

5 -o 8 


Cotang. 


10-292834 

292622 

292210 

291898 

291586 

291274 

290963 

290661 

290340 

290029 

289718 

10-289407 

289096 

288785 

288475 

288164 

287864 

287544 

287234 

286924 

286614 

io-286304 

285996 

285686 

285376 

285067 

284758 

284449 

284140 

283832 

283523 

io-2832i5 

282907 

282599 

282291 

281983 

281670 

281367 

281060 

280762 

280445 


10 


D. 


10 


Tang. 


60 

is 

57 

56 

50 
54 
53 
52 

5 1 
5 o 

49 

48 

47 

46 

45 

44 

43 

42 

4 i 

40 

39 

38 

37 

36 

35 

34 

33 

32 

3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 


• 28oi38 
279831 
279524 17 

279217 
278911 

278604 
278298 
277991 
277685 
277379 

277073 
276768 
276462 
276166 
275851 
275546 
276241 
274935 
274631 
274326 


16 

i 5 

14 

i 3 
12 
11 
10 


M. 


(62 DEGREES.) 

































































46 


(28 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9-671609 

3-96 

9-946935 

1 

12 

9-726674 

5 -o 8 

10-274326 

60 

i 

671847 

3-96 

945868 

1 

12 

725979 

5 -08 

274021 

59 

2 

672084 

3-95 

946800 

1 

12 

726284 

6-07 

273716 

08 

3 

672321 

3-95 

945733 

1 

12 

726588 

6-07 

273412 

57 

4 

672558 

3-96 

946666 

1 

12 

726892 

6-07 

273108 

56 

5 

672795 

3-94 

945598 

1 

12 

727197 

5-07 

272803 

55 

6 

673 o 32 

3-94 

94553 i 

1 

12 

727601 

5-07 

272499 

54 

7 

673268 

3-94 

946464 

1 

i 3 

727805 

5 -06 

272195 

53 

8 

6735 o 5 

3-94 

945396 

1 

i 3 

728109 

5 -06 

271891 

52 

9 

673741 

3- 9 3 

945323 

1 

j 3 

728412 

5 -06 

271588 

5 i 

IO 

673977 

3-93 

945261 

1 

i 3 

728716 

5 -06 

271284 

5 o 

11 

9-6742'! 3 

3- 9 3 

9-946193 

1 

i 3 

9-729020 

5 -06 

10-270980 

49 

I 2 

674448 

3-92 

946126 

1 

i 3 

729323 

5 -o 5 

270677 

48 

i 3 

674684 

3-92 

946068 

1 

i 3 

729626 

5 -o 5 

270374 

47 

U 

674919 

3-92 

944990 

1 

i 3 

729929 

5 -o 5 

270071 

46 

i 5 

675 i 55 

3-92 

944922 

1 

i 3 

730233 

5 -o 5 

269767 

45 

16 

675390 

3-91 

944854 

1 

i 3 

73 o 535 

5 -o 5 

269466 

44 

*7 

676624 

3-91 

944786 

1 

i 3 

73 o 838 

5 -04 

269162 

43 

18 

675859 

3-91 

9447 18 

1 

i 3 

73 ii 4 i 

5 -04 

268869 

42 

19 

676094 

3-91 

944660 

1 

i 3 

731444 

5 -o 4 

268556 

41 

20 

676828 

3-90 

944682 

1 

14 

731746 

5 -o 4 

268264 

40 

21 

9-676662 

3-90 

9-944614 

1 

14 

9-732048 

5 -04 

10-267952 

39 

22 

676796 

3-90 

944446 

1 

14 

73235 1 

5 -o 3 

267649 

38 

23 

677030 

3*90 

944377 

1 

14 

732653 

5 -o 3 

267347 

37 

24 

677264 

3 - 8 9 

944309 

1 

14 

732955 

5 -o 3 

267045 

35 

25 

677498 

3-89 

944241 

1 

U 

733267 

5 -o 3 

266743 

35 

26 

67773 i 

3 - 8 9 

944172 

1 

U 

733558 

5 -o 3 

266442 

34 

27 

677964 

3-88 

944104 

1 

14 

. 733860 

5-02 

266140 

33 

28 

678197 

3-88 

944036 

1 

14 

734162 

5-02 

265838 

32 

29 

678430 

3-88 

943967 

1 

14 

734463 

5-02 

265537 

3 i 

3 o 

678663 

3-88 

943899 

1 

14 

734764 

5-02 

265236 

3 o 

3 i 

9-678895 

3 - 8 7 

9-943830 

1 

14 

9 - 735 o 66 

5-02 

10-264934 

29 

32 

679128 

3-87 

943761 

1 

i 4 

735367 

5-02 

264633 

28 

33 

679360 

3 - 8 7 

943693 

1 

i 5 

735668 

5 -oi 

264332 

27 

34 

679692 

3 - 8 7 

943624 

1 

i 5 

735969 

5 -oi 

264031 

26 

35 

679824 

3-86 

943555 

1 

i 5 

736269 

5 -oi 

263731 

25 

36 

68 oo 56 

3-86 

943486 

1 

i 5 

736670 

5 -oi 

26343 o 

24 

37 

680288 

3-86 

943417 

1 

16 

736871 

5 -oi 

263 129 

23 

38 

680619 

3-85 

943348 

1 

i 5 

737171 

5 -oo 

262829 

22 

3 g 

680760 

3-85 

943279 

1 

16 

737471 

5 -oo 

262529 

21 

40 

680982 

3-85 

943210 

1 

1 5 

737771 

5 -oo 

262229 

20 

4 i 

9 - 68121 3 

3-85 

9 - 943 i 4 i 

1 

i 5 

9-738071 

5 -oo 

10-261929 

*9 

42 

68 i 443 

3-84 

943072 

1 

i 5 

738371 

5 -oo 

261629 

18 

43 

681674 

3-84 

943oo3 

1 

16 

738671 

4-99 

261329 

17 

44 

681905 

3-84 

942934 

1 

i 5 

738971 

4-99 

261029 

l6 

45 

682 i 35 

3-84 

942864 

1 

i 5 

739271 

4-99 

260729 

i 5 

46 

682365 

3-83 

94279 5 

1 

16 

739570 

4-99 

260430 

14 

47 

682695 

3-83 

942726 

1 

16 

739S70 

4-99 

26oi3o 

i 3 

48 

682826 

3-83 

942666 

1 

t6 

740169 

4-99 

259831 

12 

49 

633 o 55 

3-83 

942687 

1 

16 

740468 

4-98 

259532 

11 

5 o 

683 284 

3-82 

942017 

1 

16 

740767 

4-98 

259233 

10 

5 i 

o-6835i4 

3-82 

9-942448 

: 

16’ 

9-741066 

4-98 

10-258934 

0 

52 

683743 

3-82 

942378 

1 

16 

74 i 365 

4-98 

258635 

8 

53 

683972 

3-82 

9423 oS 

7 

16 

741664 

4-98 

258336 

7 

54 

684201 

3 • 81. 

942239 

I 

16 

•741962 

4*97 

258 o 38 

6 

55 

634430 

3 -81 

942169 

7 

i6 

742261 

4-97 

25 77 3 9 

5 

56 

684668 

3 - 8 i 

942099 

1 

16 

742559 

4-97 

267441 

4 

57 

684887 

3 -8o 

942029 

1 

16 

742868 

4-97 

267142 

3 

58 

685 11 5 

3 -8o 

941969 

1 

16 

743 1 56 

4-97 

266844 

a 

5 9 

685343 

3 -8o 

941889 

1 

H 

743454 

4-97 

256546 

1 

60 

680571 

3 -80 

941819 

1 

17 

743752 

4-96 

266248 

0 


! Cosine 

D. 

Sine 

I 

D. 

1 Cotang. 

! D. 

Tang. 

M. 


(61 DEGREES.) 



















































SINES AND TANGENTS. (29 DEGREES.) 47 


M. 

Sine 

‘ D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

O 


0 

9-685571 

3* 80 

9-941819 

1 • 17 

9-743702 

4-96 1 13-266248 

60 

i 

685799 

3-79 

941749 

i-*7 

744000 

4-96 

200950 

5 9 

2 

686027 

3-79 

941679 

1 • 17 

744348 

4-96 

266662 

58 

3 

686254 

3-79 

941609 

1 * *7 

744645 

4.96 

255355 

57 

4 

686482 

3-79 

941539 

1 * 17 

744943 

4.96 

200007 

56 

5 

686709 

3-78 

941469 

1*17 

745240 

4-96 

254760 

55 

6 

686936 

3-73 

941398 

1 • 17 

745538 

4-90 

254462 

54 

7 

637(63 

3 • 78 

94i328 

1 • 17 

745835 

4-90 

254(65 

53 

3 

687389 

3-78 

941268 

1-17 

746(32 

4-95 

253868 

52 

9 

687616 

3.77 

94i187 

1-17 

746429 

4-96 

253571 

5i 

10 

687843 

3-77 

941117 

1-17 

746726 

4-93 

253274 

5o 

11 

9-688069 

3.77 

9-941046 

1 • 18 

9-747023 

4-94 

10-252977 

49 

12 

688296 

3.77 

940976 

1 • 18 

747319 

4-94 

262681 

48 

i3 

688521 

3 • 76 

940906 

1 • 18 

747616 

4-94 

252334 

47 

14 

688747 

3-76 

940834 

1 • 18 

7479 l3 

4-94 

262087 

46 

i5 

688972 

3.76 

940763 

1 • 18 

748209 

4-94 

25179( 

45 

16 

689198 

3-76 

940693 

1 • 18 

7485 o 5 

4-9 3 

261495 

44 

17 

689428 

3-75 

940622 

x • 18 

748801 

4-93 

25i199 

43 

18 

689648 

3.75 

94 o 55 i 

1 • 18 

749097 

4.93 

260908 

42 

19 

689873 

3*76 

940480 

1 • 18 

74g3o3 

4.93 

260607 

4i 

20 

690098 

3*76 

940409 

1 • 18 

749689 

4.93 

25o3ii 

4o 

21 

9-690323 

3-74 

9*94o338 

X • 18 

9-749985 

4-93 

io- 25 goi 5 

3 9 

22 

690548 

3-74 

940267 

I • 18 

700281 

4-92 

249719 

38 

23 

690772 

3-74 

940196 

I • 18 

760676 

4-92 

249424 

37 

24j 

690996 

3-74 

940126 

I-I 9 

700872 

4-92 

249128 

36 

25 

691220 

3-73 

940054 

I-I 9 

701167 

4-92 

248833 

35 

26 

691444 

3-73 

939982 

I * 19 

761462 

4-9 2 

248538 

34 

27 

691668 

3-73 

939911 

1-19 

761757 

4.92 

248243 

33 

28 

691892 

3-73 

939840 

1-19 

752062 

4-9 1 

247948 

32 

29 

692115 

• 3*72' 

939068 

1 • 19 

752347 

4-91 

247653 

3i 

3o 

692339 

3-72 

939697 

1-19 

762642 

4-91 

247808 

3o 

3i 

9-692562 

3-72 

9-939625 

1-19 

9-752937 

4.9 1 

io- 247 o 63 

2 9 

32 

692786 

3-71 

939554 

1 ‘ x 9 

75323 i 

4-91 

246769 

28 

33 

693008 

3.71 

989482 

1 ’ 19 

753526 

4.91 

246474 

27 

34 

693231 

3-71 

939410 

l ‘ 19 

753820 

4.90 

246180 

26 

35 

693453 

3.71 

93q339 

i * *9 

754115 

4.90 

245885 

25 

35 

693676 

3-70 

939267 

1-20 

754409 

4.90 

240091 

24 

37 

693898 

3-70 

989196 

I -20 

754703 

4.90 

246297 

23 

33 

694120 

3-70 

939123 

I • 20 

754997 

4.90 

245oo3 

22 

3 9 

694342 

3-70 

939052 

I • 20 

755291 

4.90 

244709 

21 

40 

694564 

3-69 

938980 

I • 20 

755585 

4.89 

244415 

20 

4t 

9-694786 

3-69 

9-938908 

I • 20 

9-755878 

4.89 

10-244122 

19 

42 

696007 

3-69 

938836 

1-20 

766172 

4.89 

243828 

l8 

43 

696229 

3-69 

938763 

I -20 

766466 

4.89 

243535 

17 

44 

696460 

3-68 

938691 

I *20 

766769 

4.89 

243241 

l6 

45 

695671 

3-68 

988619 

1-20 

767062 

4.89 

242048 

i5 

46 

690892 

3-68 

988547 

1-20 

757345 

4-88 

242655 

i4 

47 

696113 

3-68 

938476 

I • 20 

767638 

4-88 

242862 

i3 

48 

696334 

3-67 

938402 

I -21 

7 5 793 i 

4-88 

242069 

12 

i 9 

696554 

3-67 

93833 o 

I -21 

768224 

4.88 

241776 

11 

5o 

696776 

3-67 

938258 

I -21 

758617 

4.88 

241483 

10 

5i 

0-6 q 6 qq 5 

3-67 

9 • g38185 

I -21 

9-758810 

4.88 

10-241190 

9 

52 

697215 

3-66 

988 n 3 

I -21 

769102 

4-87 

240898 

8 

53 

697435 

3-66 

938040 

I • 21 

769395 

4.87 

24 o 6 o 5 

7 

54 

697664 

3-66 

937967 

I -21 

759687 

4-87 

24 o 3 13 

6 

55 

697874 

3-66 

937895 

I -21 

759979 

4-87 

24002( 

5 

56 

698094 

3-65 

987822 

I -21 

760272 

4-87 

239728 

4 

57 

698318 

3-65 

937749 

I -21 

760564 

4-87 

23g436 

3 

58 

698532 

3-65 

937676. 

I -21 

760856 

4-86 

239144 

2 

5 9 

698761 

3-65 

937604 

I -21 

761148 

4-86 

238852 

1 

60 

698970 

3*64 

937531 

I -21 

761439 

4-86 

238561 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


27 (60 DEGREES.) 


I 


















































48 (30 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

- P 

D. 

— -- 

Cotang. 


' 0 

9-698970 

3-64 

9-937531 

I -21 

9-761439 

4-86 

io- 23856 i 

60 

i 

699189 

3-64 

937458 

1-22 

761731 

4-86 

238269 

5 q 

2 

699407 

3-64 

937385 

1-22 

762023 

4-86 

237977 

58 

3 

699626 

3-64 

937312 

1-22 

762314 

4-86 

237686 

5 7 

4 

699844 

3-63 

937238 

1-22 

1-22 

762606 

4-85 

237394 

56 

5 

700062 

3-63 

937165 

762897 

4-85 

237103 

55 

6 

700280 

3-63 

937092 

1-22 

763188 

4-85 

236812 

54 - 

7 

700498 

3-63 

937019 

I -22 

7634-9 

4-85 

236521 

53 

8 

700716 

3-63 

936946 

1-22 

763770 

4-85 

23623 o 

52 

9 

700933 

3-62 

936872 

1-22 

764.061 

4-85 

230989 

5 i 

10 

7011 5 i 

3-62 

936799 

I • 22 

764352 

4-84 

235648 

5 o 

ii 

9-701368 

3-62 

9-936725 

I -22 

9•764643 

4-84 

10-235357 

49 

12 

70 i 585 

3-62 

986662 

I • 23 

764933 

4-84 

235067 

48 

i 3 

701802 

3 • 61 

936578 

1-23 

766224 

4-84 

234776 

47 

14 

702019 

3 -61 

9365 o 5 

1-23 

7655 i 4 

4-84 

234486 

46 

i 5 

702236 

3 * 6 i 

93643 i 

1-23 

7658o5 

4-84 

234195 

45 

16 

702452 

3 - 6 i 

936357 

1-23 

766095 

4-84 

233905 

44 

n 

702669 

702880 

3 -6o 

936284 

I -23 

766385 

4-83 

2336 i 5 

43 

18 

3 -60 

936210 

1-23 

766675 

4-83 

233325 

42 

*9 

7 o 3 ioi 

3 -6o 

g 36 1 36 

I -23 

766965 

4-83 

233 o 35 

41 

20 

703317 

3 -60 

936062 

I • 23 

767255 

4-83 

232745 

40 

21 

9-703533 

3 - 5 9 

9-936988 

1-23 

9-767645 

4-83 

10-232455 

3 o 

22 

703749 

3 - 5 9 

935914 

935840 

1-23 

767834 

4-83 

232166 

38 

23 

703964 

3 - 5 9 

I • 23 

768124 

4-82 

231876 

37 

24 

704179 

3 - 5 9 

935766 

1-24 

768413 

4-82 

23 1587 

36 

25 

704395 

3 - 5 9 

935692 

1-24 

768703 

4-82 

231297 

35 

26 

704610 

3-58 

9 356 i 8 

I • 24 

768992 

3-82 

23 ioo 8 

34 

27 

704S25 

3-58 

935543 

1-24 

769281 

4-82 

230719 

33 

28 

705040 

3-58 

986469 

1-24 

769570 

4-82 

23 o 43 o 

32 

29 

705254 

3-58 

935896 

1-24 

769860 

4-8i 

23 oi 4 o 

3 i 

3 o 

705469 

3-57 

935320 

1-24 

77 OI 4 S 

4-8i 

22 Q 852 

3 o 

3 i 

g- 7 o 5683 

3-57 

9-935246 

I • 24 

9-770437 

4-8i 

10-229563 

29 

32 

705898 

3-57 

935171 

1-24 

770726 

4-81 

229274 

228985 

28 

33 

706112 

3-57 

935097 

1-24 

771015 

4-8i 

27 

34 

706326 

3-56 

935022 

1-24 

77i3o3 

4-8i 

228697 

26 

35 

706539 

3-56 

934948 

1-24 

771692 

4-8i 

228408 

25 

36 

706753 

3-56 

934873 

1-24 

771880 

4-8o 

228120 

24 

37 

706967 

3-56 

934798 

1-25 

772168 

4-80 

227832 

23 

38 

707180 

3-55 

934723 

1-25 

772457 

4 -80 

227543 

22 

39 

707393 

3-55 

934649 

1-25 

772745 

4-8o 

227255 

21 

40 

707606 

3-55 

934574 

1-25 

773 o 33 

4 - 8 o 

226967 

20 

41 

9-707819 

3-55 

9-934499 

I • 25 

9-773321 

4 -80 

10-226679 

IO 

42 

708032 

3-54 

984424 

1-25 

773608 

4-79 

226392 

10 

4.3 

708245 

3-54 

934349 

1-25 

773896 

774184 

4-79 

226104 

17 

44 

708458 

3-54 

934274 

1-25 

4-79 

226816 

l6 

45 

708670 

3-54 

984199 

I -25 

774471 

4-79 

226629 

i 5 

46 

708882 

3-53 

934123 

1-25 

774759 

4-79 

226241 

14 

47 

709094 

3-53 

934048 

1-25 

775046 

4-79 

224964 

i 3 

48 

7og3o6 

3-53 

933973 

933898 

I • 25 

775333 

4-79 

224667 

12 

49 

709618 

3-53 

I -26 

776621 

4-78 

224379 

11 

5 o 

709730 

3 - 53 

933822 

I -26 

776908 

4-78 

224092 

10 

5 i 

9 - 7099 -II 

3-52 

9-933747 

1-26 

9-776195 

4-78 

io- 2238 o 5 

Q 

52 

7ioi53 

3*52 

933671 

1-26 

776482 

4-78 

2235 i 8 

8 

53 

710364 

3-52 

988696 

I -26 

776760 

4-78 

223231 

7 

54 

710676 

3-52 

983520 

1-26 

777 o 55 

4-78 

222945 

6 

55 

710786 

3 - 5 i 

983440 

I • 26 

777.342 

4-78 

222658 

5 

56 

5 7 

710997 

711208 

3 - 5 i 

3 • 5 1 

933369 

933293 

1-26 

I • 26 

777628 

777915 

4-77 

4-77 

222372 

222085 

4 

3 

58 

711419 

3 * 5 i 

933217 

I ■ 26 

778201 

4-77 

221799 

2 

09 

711629 

3 - 5 o 

g 33 i 4 i 

I • 26 

778487 

4-77 

2 215 l 2 

1 

60 

711839 

3 - 5 o 

933o66 

1-26 

778774 

4-77 

221226 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

-2_1 

M. 


(59 DEGREES.) 




































































C'C7\C7iC7'0<UiC7lcnCJ>0l ^WWWWCjJWWWW OJlOUMUIOtOIOlOK) io>—1— 

O -O CC-J O' Wx+^ Om n O O OO— J O' coii*. CO to t-t O O CO-4 O' Oi£s Co to 4-1 0-0 00 — 1 O' OKI H O O 00—1 O' Oi^ Co w >- O 'O 


SINES AND TANGENTS. (31 DEGREES.) 


49 


M. 


0 

1 

2 

3 

4 

5 

6 


Sine 

D. 

Cosine 

D. 

Tang. D. 

Cotang. 


9-711839 

7i2o5o 

712260 

712469 

712679 

712889 

713098 

7i33o8 

71 35 17 
713726 
713935 

9 - 7 i 4 i 44 

714352 

714361 

714769 

714978 

71 5 i86 

715394 

715602 

716809 

716017 

9-716224 

716432 

716639 

716846 

717053 

717269 

717466 

717673 

717879 

718085 

9-718291 

718497 
718703 
718909 
7191i 4 
719320 
719626 
719730 
719935 
720140 

9-720345 
720649 
720754 
720958 
721162 
721 366 
721670 
721774 

721978 

722181 

9*722385 

722588 

722791 

722994 

723197 

723400 

7236 o 3 

728806 

724007 

724210 

3 - 5 o 
3 - 5 o 
3 - 5 o 
3-49 
3-49 
3-49 
3-49 
3-49 
3-48 
3-48 
3-48 

3.48 

3-47 

3-47 

3-47 

3-47 

3-47 

3-46 

3-46 

3-46 

3-46 

3-45 

3-45 

3-45 

3-45 

3.45 

3 -44 
3-44 

3 -44 
3-44 
3-43 

3-43 

3-43 

3-43 

3-43 

3-42 

3-42 

3-42 

3-42 

3 - 4 i 

3 - 4 i 

3 - 4 i 

3 - 4 x 

3 -40 

3 -40 
3 - 4 o 
3 - 4 o 
3 - 4 o 

3 - 3 9 
3 - 3 9 
3 - 3 9 

3 - 3 9 
3 - 3 9 
3-38 
3-38 
3-38 
3-38 
3-37 
3-37 
3 - 3 7 
3-3 7 

9-933066 

932990 

932914 

9 32838 

932762 

932685 

932609 

932533 

932457 

93238 o 

9323 o 4 

9-932228 
932161 
932075 
981998 
931921 
931 845 
931768 
931691 
931614 
93 i 537 

9-931460 
931 383 
93 i 3 o 6 
931229 

9311 52 

931075 

930998 

930921 

930843 

930766 

9-930688 
930611 
93 o 533 
93 o 456 
g 3 o 3 -]S 
93 o 3 oo 
93 o 223 
93 oi 45 
930067 
929989 

9-929911 
929833 
929755 
929677 
929699 
929621 
929442 
929364 

929286 

929207 

9-929129 

929050 

928972 

928893 

928815 

928736 

928657 

928578 

928499 

928420 

1-26 

1 • 27 

1 -27 

1 • 27 
1*27 
i • 27 

1 -27 

1 -27 

1 -27 
1-27 
1-27 

1*27 

1-27 

1 -28 

1 ■ 28 

1 • 28 
1-28 

1 • 28 
1-28 
1-28 

1 • 28 

1-28 

1-28 

1 -28 
1-29 
1-29 

1 -29 
1-29 
1-29 

1 • 29 
1-29 

1 -29 
1-29 
1-29 

1 • 29 

1 -29 

1 - 3 o 

1 - 3 o 

1 -3o 
r - 3 o 

1 - 3 o 

1 -3o 

1 -3o 

1 »3o 

1 -3o 

1 - 3 o 

1 - 3 o 
i- 3 o 

1 • 3 1 

1 • 3 x 

1 - 3 i 

1 • 3 1 

1 • 3 1 
i- 3 i 

1 • 3 1 

1 - 3 i 

1 - 3 i 

1 • 3 1 

1 * 3 1 

1 • 3 1 

1 • 3 1 

9-778774 

779060 

779 3 46 

779632 

779918 

780203 

780489 

780775 

781060 

781346 

781631 

9-781916 

782201 

782486 

782771 

783 o 56 

783341 

783626 

783910 

784195 

784479 

9-784764 

786048 

785332 

7856 i 6 

785900 

786184 

786468 

786752 

787036 

787319 

9-787603 

787886 

788170 

788453 

788736 

789019 

789302 

789585 

789868 

790151 

9-790433 
790716 
790999 
791281 
791 563 
791846 
792128 
792410 
792692 
792974 

9-793266 

793533 

793819 

794.101 

794383 

794664 

794945 

796227 

7955 o 8 

796789 

4-77 

4-77 

4-76 

4-76 

4-76 

4-76 

4-76 

4-76 

4-76 

4-75 

4 - 7 5 

4-75 

4-75 

4-75 

4-75 

4-75 

4-75 

4-74 

4-74 

4-74 

4-74 

4-74 

4-74 

4-73 

4-73 

4-73 

4-73 

4-73 

4-73 

4-73 

4-72 

4-72 

4-72 

4-72 

4-72 

4-72 

4-72 

4-71 

4-71 

4-71 

4-71 

4-71 

4-71 

4-71 

4-71 

4-70 

4-70 

4-70 

4-70 

4-70 

4-70 

4-70 

4-69 

4-69 

4-69 

4-69 

4-69 

4-69 

4-6 q 

4-68 

4-68 

10-221226 
220940 
220664 
220368 
220082 
219797 
219511 
219225 
218940 

21 8654 
218369 

10-218084 

217799 

217514 

217229 

216944 

216659 

216374 

216090 

2 i 58 o 5 

21 552 1 

io- 2 i 5236 
214952 
214668 
214384 
214100 

21 38 16 

21 353 2 
213248 
212964 
212681 

10-212397 
212114 

2 ii 83 o 

211547 
211264 

210981 

210698 

2io4i5 

210 x 32 

209849 

10-209567 
209284 
209001 
20S719 
208437 
208154 

207872 

207590 

207308 

207026 

10-206744 

206462 

206181 

205899 

206617 

2 o 5336 

2 o 5 o 55 

204773 

204492 

204211 

60 

5 9 

58 

57 

56 

55 

54 

53 

52 

5 i 

5 o 

49 

48 

47 - 

46 

45 

44 

43 

42 

4 i 

4 o 

39 

38 

37 

36 

35 

34 

33 

32 

3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

i 5 

i 4 

i 3 

12 

11 

10 

9 

8 

7 

6 

’ 5 

4 

3 

2 

1 

0 

Cosine 

D. 

Sine 

D. i Cotang. 

D. 

Tang. 

M. 


% 


(58 DEGREES.) 











































50 (32 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-724210 

3-37 

9-928420 

I -32 

9-795789 

4-68 

10-204211 

60 

i 

724412 

3-37 

928342 

1-32 

796070 

4-68 

203930 

5 9 

2 

724614 

3-36 

928263 

1-32 

79635 i 

4-68 

203649 

58 

3 

724816 

3-36 

928183 

I -32 

796632 

4-68 

2 o 3368 

57 

4 

725017 

3-36 

928104 

1-32 

796913 

4-68 

203087 

56 

5 

725219 

3-36 

928025 

I -32 

797194 

4-68 

202806 

55 

6 

" 725420 

3-35 

927946 

1-32 

79747 ° 

4-68 

202525 

54 

7 

725622 

3-35 

927867 

1-32 

797750 

4-68 

202245 

53 

8 

725823 

3-35 

927787 

I -32 

798036 

4-67 

201964 

52 

9 

726024 

3-35 

927708 

1-32 

798316 

4-67 

201684 

5 i 

10 

726226 

3-35 

927629 

I -32 

798696 

4-67 

201404 

5 o 

11 

9-726426 

3-34 

9-927549 

I -32 

9-798877 

4-67 

10 - 201123 

49 

12 

726626 

3-34 

92747° 

1-33 

799157 

4-67 

200843 

48 

i 3 

726827 

3-34 

927390 

i -33 

799437 

4-67 

2 oo 563 

47 

i 4 

727027 

3-34 

927310 

i -33 

799717 

4-67 

200283 

46 

i 5 

727228 

3-34 

927231 

i -33 

799997 

4-66 

200003 

40 

16 

727428 

3-33 

927151 

i -33 

800277 

4-66 

199723- 

44 

17 

727628 

3-33 

927071 

i -33 

800507 

4-66 

199443 

43 

18 

727828 

3-33 

926991 

i -33 

8 oo 836 

4-66 

199164 

42 

19 

728027 

3-33 

926911 

i -33 

801116 

4-66 

198884 

41 

20 

728227 

3-33 

92683 i 

i -33 

801396 

4-66 

198604 

40 

21 

9-728427 

3-32 

9-926751 

i -33 

9-801675 

4-66 

10-198325 

39 

22 

728626 

3-32 

926671 

i -33 

801965 

4-66 

198045 

38 

23 

728825 

3-32 

926691 

i -33 

802234 

4-65 

197766 

37 

24 

729024 

3-32 

9265 ii 

i -34 

8 o 25 i 3 

4-65 

197487 

36 

25 

729223 

3 - 3 i 

926431 

1 • 34 

802792 

4-65 

197208 

35 

26 

729422 

3 - 3 x 

92635 i 

i -34 

803072 

4-65 

196928 

34 

27 

729621 

3 • 3 1 

926270 

i -34 

8 o 335 i 

4-65 

196649 

33 

28 

729820 

3 • 3 1 

926190 

i -34 

8 o 363 o 

4-65 

196370 

32 

29 

730018 

3 - 3 o 

926110 

i -34 

803908 

4-65 

196092 

3 i 

3 o 

730216 

3 - 3 o 

926029 

i -34 

804187 

4-65 

I 958 i 3 

3 o 

3 i 

9-73041 5 

3 - 3 o 

9-926949 

i -?4 

9•804466 

4-64 

10-195534 

29 

32 

73o6i3 

3 - 3 o 

925868 

1 -4 

8 o 4745 

4-64 

195255 

28 

33 

73 o 8 i1 

3 - 3 o 

925788 

1 -34 

8 o 5 o 23 

4-64 

194977 

27 

34 

731009 

3 • 29 

925707 

1 -34 

8 o 53 o 2 

4-64 

194698 

26 

35 

731206 

3 • 29 

925626 

1 -34 

8 o 558 o 

4-64 

194420 

25 

36 

73 i 4 o 4 

3 • 29 

925545 

1 -35 

805809 

4-64 

194141 

24 

37 

731602 

3 • 29 

925465 

1 -35 

806137 

4-64 

iq 3863 

23 

38 

731799 

3 • 29 

925384 

i -35 

806410 

4-63 

193585 

22 

39 

731996 

3-28 

9253 o 3 

1 -35 

806693 

4-63 

193307 

21 

4 o 

732193 

3-28 

925222 

1 -35 

806971 

4-63 

193029 

20 

4 i 

9-732390 

3-28 

9-925141 

i -35 

9-807249 

4-63 

io-192751 

*9 

42 

732087 

3-28 

926060 

i -35 

807527 

4-63 

192473 

18 

43 

732784 

3-28 

924979 

1 -35 

807800 

4-63 

192195 

17 

44 

732980 

3-27 

924897 

i -35 

8 o 8 o 83 

4-63 

1919*7 

16 

45 

733177 

3-27 

924816 

i -35 

8 oS 36 i 

4-63 

191639 

i 5 

46 

733373 

3-27 

924735 

i -36 

8 o 8638 

4-62 

191362 

14 

47 

733569 

3-27 

924654 

i -36 

808916 

4-62 

191084 

i 3 

48 

733760 

3-27 

924572 

i -36 

809193 

4-62 

190807 

12 

49 

733961 

3-26 

924491 

i -36 

809471 

4-62 

190529 

11 

5 o 

734 i 57 

3-26 

924409 

i -36 

809748 

4-62 

190252 

10 

5 i 

9-734353 

3-26 

9-924328 

i -36 

9-810026 

4-62 

10-189975 

9 

52 

734049 

3-26 

924246 

i -36 

8 io 3 o 2 

4-62 

189698 

8 ' 

53 

734744 

3-25 

924164 

i -36 

8 io 58 o 

4-62 

189420 

7 

54 

734989. 

3-25 

924 o 83 

i -36 

810867 

4-62 

189143 

6 

55 ‘ 

735 1 35 

3-25 

924001 

i -36 

8111 34 

4-61 

188866 

5 

56 

73533 o 

3-25 

923919 

i -36 

811410 

4 - 6 i 

188590 

4 

57 

735525 

3-25 

923837 

i -36 

811687 

4-6 i 

1 883 1 3 

3 

58 

735719 

3-24 

923755 

1.37 

811964 

4-6 i 

i 88 o 36 

2 

5 9 

735914 

3-24 

923673 

i -3 7 

812241 

4-6 i 

187759 

1 

60 

736109 

3-24 

923591 

1-37 

812517 

4 - 6 i 

187483 

0 

! 


| Cosine 

1 D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(57 DEGREES.) 























































.&■. COCOCOCOCOCJGJCOGJ UUMMUMUMUM IO>—• M 

O sO CO—J OOiJX Wio x O O CO-4 O'Cn^OJto— 0-0 GO-4 C>Wi4i\ Oju -i OvO 00—1 O'WMiJtJ m O O 00-4 O' U> 4^ GJ (4 -• OO CO-J O C* JX GJ (O 


SINES AND TANGENTS. (33 DEGREES.) 51 


Sine 

r>- 1 

! 

Cosine 

D. 

Tang. 

D. 

Cotang. 


9-736109 

3-24 

9 - 9*3 5 9 i 

1-37 

9-812517 

4-6 i 

io-187482 

60 

7363 o 3 

3-24 

923509 

1-37 

812794 

4-61 

187206 

5 g 

736498 

3-24 

923427 


813070 

4 • 61 

186930 

58 

736692 

736886 

3-23 

923345 

1.37 

813347 

4-6c 

186653 

57 

3-23 

923263 

i- 3 7 

8 i 3623 

4-6c 

186377 

56 

737080 

3-23 

923181 

i- 3 7 

813899 

4-60 

186101 

55 

737274 

3-23 

923098 

1-37 

814176 

4-6c 

1 85825 

54 

737467 

3-23 

923016 

i- 3 7 

814462 

4-60 

185548 

185272 

53 

737661 

3-22 

922 o 33 

922851 

i- 3 7 

814728 

4-60 

52 

737855 

738048 

3-22 

1-37 

816004 

4-60 

184996 

5 i 

3-22 

922768 

i -38 

816279 

4-60 

184721 

5 o 

9-738241 

3-22 

9-922686 

i -38 

9-81 5555 

4-59 

io-i 84445 

4 q 

738434 

3-22 

922603 

i -38 

81 583 1 

4-59 

184169 

48 

738627 

8-21 

922520 

i -38 

816107 

4-59 

183896 

47 

738820 

3-21 

922438 

i -38 

81 6382 

4-59 

1 836 18 

46 

739013 

3*21 

922355 

i -38 

81 6658 

4 - 5 9 

i 83342 

45 

739206 

3-21 

922272 

i -38 

816933 

4-59 

183067 

44 

739398 

3-21 

922189 

i -38 

817209 

4-59 

182791 

43 

739590 

739783 

3-20 

922106 

i -38 

817484 

4 - 5 g 

i 825 i 6 

42 

3-20 

922023 

i -38 

817759 

4 - 5 o 

182241 

4 i 

739975 

3 • 20 

921940 

i *38 

8 i 8 o 36 

4-58 

181965 

40 

9-740167 

3-20 

9-921857 

1 -39 

9 - 8 i 83 io 

4-58 

io-181690 

3 9 

740359 

3-20 

921774 

1 -39 

81 8585 

4-58 

18141 5 

38 

74 o 55 o 

3 -19 

921691 

1 -39 

818860 

4 - 58 . 

181140 

37 

740742 

3 • 19 

921607 

1 -39 

819135 

4-58 

i 8 o 865 

36 

740934 

3-19 

921624 

1 -39 

819410 

4-58 

180590 

35 

74 H 25 

3-19 

921441 

1 -39 

819684 

4-58 

i 8 o 3 i 6 

34 

74 i 3 i 6 

3-19 

921357 

1 -39 

819969 

4-58 

180041 

33 

74 i 5 o 8 

3 -i 8 

921274 

1-39 

820234 

4-58 

179766 

32 

741699 

3 -18 

921190 

1 -39 

82 o 5 o 8 

4.57 

179492 

3 i 

741889 

3 -i 8 

921107 

1-39 

820783 

4-57 

1 79 21 7 

3 o 

9-742080 

3 *i 8 

9-921023 

1 -39 

9-821067 

4.57 

10-178943 

29 

742271 

3 *i 8 

920939 

1 - 4 o 

821332 

4.57 

178668 

28 

742462 

3-17 

920856 

1 - 4 o 

821606 

4-57 

178394 

27 

742652 

3-17 

920772 

1 - 4 o 

821880 

4.57 

178120 

26 

742842 

3-17 

920688 

1 - 4 o 

822154 

4-57 

177846 

25 

743 o 33 

3-17 

920604 

1 - 4 o 

822429 

4-57 

i 77 5 7 i 

24 

743223 

3-17 

920520 

1 • 40 

822706 

4.57 

177297 

23 

7434 i 3 

3 -16 

920436 

i- 4 o 

822977 

4-56 

177023 

22 

743602 

3 -16 

920352 

1 • 40 

823260 

4-56 

176750 

21 

743792 

3 -16 

920268 

1 - 4 o 

823524 

4-56 

176476 

20 

9-743982 

3 • 16 

9-920184 

i- 4 o 

9-823798 

4-56 

10-176202 

I9 

74417 1 

3 -16 

920099 

1 - 4 o 

824072 

4-56 

175928 

l8 

74436 i 

3 • 1 5 

920016 

1 - 4 o 

824345 

4-56 

175655 

17 

74455o 

3 • 1 5 

919031 

919846 

1 - 4 i 

824619 

4-56 

175381 

l6 

744739 

3 • 1 5 

1 - 4 i 

824896 

4-56 

175107 

i 5 

744928 

3 • 1 5 

919762 

1*41 

826166 

4-56 

174834 

r 4 

745117 

3 • 1 5 

919677 

1 * 4 i 

825439 

4-55 

174561 

i 3 

7453o6 

3 • 14 

919593 

i- 4 i 

825716 

4-55 

174287 

12 

745494 

3 -14 

919608 

1 * 4 i 

825986 

4-55 

174014 

11 

745683 

3 -i 4 

919424 

1 - 4 i 

826259 

4-55 

173741 

10 

9-746871 

3 -14 

9-919339 

1 * 4 i 

9-826532 

4-55 

10-173468 

9 

746069 

3 • 14 

919254 

1 - 4 i 

826806 

4-55 

173196 

8 

746248 

3 • 1 3 

919169 

1-41 

827078 

4-55 

172922 

7 

746436 

4-13 

919086 

i- 4 i 

827351 

4-55 

172649 

6 

746624 

3 -13 

919000 

918915 

9i883o 

918745 

1 * 4 i 

827624 

4-55 

172376 

5 

746812 

3 -1 3 

I -42 

827897 

4-54 

172103 

4 

746999 

747187 

3 -i 3 

3-12 

1-42 

1-42 

828170 

828442 

4-54 

4-54 

171830 

I 7 i 558 

3 

2 

747374 

3-12 

918669 

1 -42 

828715 

4-54 

171285 

1 

747562 

3-12 

918674 

1-42 

828987 

4-54 

171013 

0 

Cosine 

D. 

Sine 

D. 

Co tang. 

D. 

Tang. 

M. 


18 (56 DEGREES.) 






































52 


(34 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

2 9 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

S 

51 

52 

53 

54 

55 

56 

$7 

58 

i 9 o 

9-747562 
747749 - 
747936 

748123 

7483 io 

748497 

748683 

748870 

749056 

749243 

749429 

9-749616 

749801 

7499 8 7 

750172 

75o358 

75 o 543 

750729 

750914 

751009 

751284 

9-761469 

75 i 654 

751839 

752023 

752208 

752392 

752576 

762760 

752944 

753128 

9-7533i2 

753495 

753679 

753862 

764046 

754229 

754412 

754695 

754778 

704960 

9-755 i 43 

755326 

7555o8 

755690 

755872 

756 o 54 

756236 

756418 

766600 

756782 

9-756963 

767144 

757326 

757507 

757688 

757869 

758 o 5 o 

75823 o 

758411 
758691 

3-12 

3-12 

3-12 

3-ii* 

3-11 

3-u 

3-11 

3-11 

3-10 
3-io 
3-io 

3-10 

3-10 
3-09 
3-09 
3-09 
3-09 
3-o 9 

3-08 

3- 08 

3-08 

3-08 

3-08 

3-08 
3-07 
3-07 
3-07 
3-07 
3-07 

3-06 

3-06 

3-06 

3 -06 

3-06 

3-o5 

3-o5 

3-o5 

3-o5 . 

3-o5 

3-o4 

3-o4 

3-04 
3-o4 

3 -o4 

3-04 
3-o3 

3 -o3 
3-o3 
3-o3 
3-o3 
3-02 

3-02 

3-02 

3-02 

3-02 

3-oi 

3-oi 

3-oi 

3-oi 

3-or 

3-oi 

9-918674 

918489 

918404 

918318 
918233 
918147 

918062 

917976 

917891 

917805 

917719 

9-917634 

917648 

917462 

917376 

917290 

917204 
917118 
917032 

916946 
916859 

9‘9 1 6773 
916687 
916600 

916514 
916427 
916341 
916254 
916167 
916081 

915994 

9'9 i 59°7 

916820 

9i5733 

915646 

9i5559 

915472 

915385 
915297 
915210 

915123 

9-9i5o35 

914948 

914860 

914773 

914685 

914598 

914510 

914422 

914334 

914246 

9-914158 

914070 

913982 

913894 

913806 

913718 

9i363o 

9i354i 

9i3453 

913365 

1-42 

1-42 

I -42 

I -42 

I -42 
1-42 

I -42 

1 -43 

1 -43 
1-43 

1 -43 

1-43 

1 -43 

1 -43 

1 -43 

1 -43 

1 -43 

1 -44 
i-44 
1-44 
i-44 

1 -44 
i-44 
i-44 

1 -44 
i-44 
i-44 
i-44 
i -45 

1 -45 

1 -45 

1 -45 

1 -45 

1 -45 

1 -45 

1 -45 

1 -45 
1-45 

1 -45 
1-45 

1 -46 

1 -46 

1 -46 

1 -46 

1 -46 
1-46 

1 -46 

1 -46 

1 -46 

1 -46 
i-47 

i-47 
i-47 
i-47 
i-47 
i-47 
i-47 
x-47 
1-47 
i-47 
i-47 

9-828987 
8^9260 
829532 
829806 
830077 
83o349 
83o62i 
830893 
831165 
83i437 
831709 

9-831981 
832253 
832525 
832796 
833o68 
83333 9 
833611 
833882 
834i54 
834425 

9•834696 
834967 
835238 
835509 
835780 
836o5i 
836322 
8365 9 3 
836864 
837134 

9-8374 o 5 

837675 

837946 

838216 

838487 

838 7 5 7 

839027 

839297 

83 9 568 

839838 

9-840108 

840378 

840647 

840917 

841187 

841457 

841726 

841996 

842266 

842535 

9-842805 
843074 
843343 
843612 
843882 
84415i 
844420 
844689 
844958 
846227 

4-54 

4-54 

4-54 

4-54 

4-54 

4-53 

4-53 

4-53 

4-53 

4-53 

4-53 

4-53 

4-53 

4-53 

4-53 

4-52 

4-52 

4-52 

4-52 

4-52 

4-52 

4-52 

4-52 

4-52 

4-52 

4-5 i 

4 • 51 
4-5 i 
4-5 i 

4 • 51 
4-5 i 

4-5 i 

4-5 i 

4 • 51 

4 • 51 

4- 5o 
4-5 o 
4-5 o 
4-5 o 
4-5 o 
4-5 o 

4-5 o 

4-5 o 

4-5 o 

4-49 

4-49 

4-49 

4-49 

4-49 

4-49 

4-49 

4-49 

4-49 

4-49 

4-49 

4-48 

4-48 

4-48 

4-48 

4-48 

4-48 

io-171013 

170740 

170468 

170196 

169923 

169651 

169379 

369107 

i68835 

168563 

168291 

io-168019 

J 67747 

167476 

167204 

166932 

166661 
i6638o 

166118 
166846 
165575 

io-i 653o4 
i65o33 
164762 

164491 
164220 
163949 
163678 
163407 

163136 
162866 

io-162595 
162325 

162054 

161784 

161513 

161243 

160973 

160703 

160432 

160162 

10-159892 

159622 

169353 

169083 

158813 
168643 
158274 
i58oo4 

157734 

157466 

10-157195 

156926 

156657 
156388 

1561i8 
155849 
i5558o 

1553 11 
i 55 o 42 

154773 


Cosine 

D. 

1 Sine 

D. 

Cotang. 

D. 

Tang. 


i 





(55 DEGREES.) 


— fotoioiosjfotoiotoio OJWUWCOWOJWWW OlO>CJ>OlC^O)t7>e7iOlO>0 

OHM WJN m ON—1 COnO O " IO Ui O'—I COnO o l - 1 >0 OJ^ Of> O'—I COnO o >1 to Co CJ >1 O'—4 CC-O o « »J « 0—1 OOnO o 














































SINES AND TANGENTS. (35 DEGREES.) 


53 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9 * 7585 9 i 

3 -oi 

9-91 3365 

1.47 

9-845227 

4.48 

10-154773 

60 

i 

708772 

3 -oo 

913276 

1*47 

845496 

4.48 

154604 

5 9 

2 

758 9 52 

3 -oo 

913187 

1-48 

846764 

4.48 

1 54236 

58 

3 

709132 

3 -oo 

913099 

1-48 

846 o 33 

4.48 

153967 

5 ~i 

4 

75 9 3 i 2 

3 -oo 

9 i 3 oio 

1 -48 

846302 

4.48 

153698 

56 

5 

769492 

3 -oo 

912922 

1 -48 

846670 

4-47 

1 5343 o 

55 

6 

709672 

2-99 

912833 

1-48 

846839 

4-47 

1 53 161 

54 

I 

759862 

2-99 

912744 

1 -48 

847107 

4-47 

152893 

53 

8 

760031 

2-99 

912655 

1 -48 

847376 

4-47 

152624 

52 

9 

760211 

2-99 

9 i 2566 

1 -48 

847644 

4-47 

1 52356 

5 i 

IO 

760390 

2-99 

9 12 477 

1 • 48 

84791 3 

4-47 

162087 

5 o 

11 

9-760569 

2-98 

9-9123S8 

1 -48 

9•84818i 

4-47 

io-161819 

49 

12 

760748 

2-98 

912299 

1*49 

848449 

4-47 

1 5 1 55 1 

48 

i 3 

760927 

2-98 

912210 

1 -49 

848717 

4-47 

1 5 1 233 

47 

14 

761106 

2-98 

912121 

1 - 4 9 

848986 

4-47 

1 5 1014 

46 

i 5 

761285 

2-98 

912031 

1-49 

849204 

4-47 

160746 

45 

16 

761464 

2-98 

911942 

i- 4 9 

849022 

4-47 

160478 

44 

*7 

761642 

2-97 

91i 853 

i- 4 9 

849790 

4-46 

i 5 o 2 IO 

43 

18 

761821 

2-97 

911763 

1 -49 

85 oo 58 

4-46 

149942 

42 

»9 

761999 

2-97 

911674 

1 -4 9 

85 o 325 

4-46 

149675 

41 

20 

762177 

2-97 

911584 

i- 4 9 

85 o 593 

4.46 

149407 

40 

21 

9-762356 

2-97 

9*911 4 9 5 

1 - 4 9 

9 - 85 o 86 i 

4.46 

10-149139 

3 9 

22 

762534 

2-96 

911400 

1 - 4 9 

85 1129 

4.46 

148871 

38 

23 

762712 

2-96 

911 3 1 5 

1 - 5 o 

85 1 3 9 6 

4-46 

I48604 

37 

24 

762889 

2-96 

911226 

1 - 5 o 

85 1664 

4.46 

148336 

36 

25 

763067 

2-96 

9111 36 

1 - 5 o 

8 oi 9 3 i 

4-46 

148069 

35 

26 

763245 

2-96 

911046 

1 - 5 o 

862199 

4-46 

147801 

34 

27 

763422 

2-96 

910906 

1 - 5 o 

862466 

4.46 

147534 

33 

28 

763600 

2- 9 5 

910866 

1 - 5 o 

852733 

4-40 

147267 

32 

o 9 

763777 

2 - 9 5 

910776 

1 - 5 o 

853 001 

4-45 

146999 

3 i 

3 o 

763954 

2- 9 5 

910686 

1 • 5 o 

853268 

4-45 

146702 

3 o 

3 i 

9-764131 

2- 9 5 

9 - 9 io 5 9 6 

1 - 5 o 

9-853535 

4-45 

io-146465 

29 

32 

764308 

2- 9 5 

9 io 5 o 6 

1 - 5 o 

853802 

4-40 

146198 

28 

33 

764485 

2-94 

9 io 4 1 5 

1 - 5 o 

854069 

4-45 

i 4 d 9 3 1 

27 

34 

764662 

2-94 

9 io 325 

1 • 5 1 

854336 

4*45 

145664 

26 

35 

764838 

2-94 

910235 

i - 5 1 

854603 

4-45 

145397 

25 

36 

765 oi 5 

2-94 

9101 44 

1 - 5 i 

854870 

4-45 

i 45 i 3 o 

24 

o 7 

766191 

2- 94 

910054 

1 - 51 

850137 

4-45 

144863 

23 

33 

765367 

2-94 

909963 

1 • 5 1 

855404 

4-45 

144696 

22 

3 9 

765544 

2 • 9 3 

909878 

1 • 5 1 

855671 

4-44 

144329 

21 

4 o 

765720 

2.93 

909782 

1 - 5 1 

855 9 38 

4-44 

144062 

20 

4 i 

9-765896 

2 - 9 3 

9-909691 

1 - 5 1 

9-856204 

4-44 

10-143796 

19 

42 

766072 

2 - 9 3 

909601 

1 • 5 1 

85647 1 

4-44 

143029 

18 

43 

766247 

2 • 9 3 

909610 

1 - 5 i 

866737 

4-44 

143263 

17 

44 

766423 

2 - 9 3 

909419 

1 - 5 i 

867004 

4-44 

142996 

l6 

45 

766698 

2-92 

909328 

I -52 

857270 

4-44 

142730 

i 5 

46 

766774 

2-92 

909237 

I -52 

867537 

4-44 

142463 

14 

47 

766949 

2-92 

909146 

I -52 

867803 

4-44 

142197 

i 3 

48 

767124 

2 - 9 2 

909065 

1 -52 

868069 

4-44 

i 4 i 9 3 i 

12 

49 

767300 

2-92 

908964 

1-52 

858336 

4-44 

141664 

11 

5 o 

767475 

2-91 

90887 3 

I -52 

8586 o 2 

4-43 

141398 

10 

5 i 

9-767649 

2-91 

9-908781 

I -52 

9-858868 

4-43 

io-141132 

0 

52 

767824 

2-91 

908690 

1-52 

869134 

4-43 

140866 

8 

53 

767999 

2-91 

908599 

I -52 

809400 

4-43 

140600 

7 

54 

768173 

2-91 

908507 

I -52 

85 9 666 

4-43 

i 4 o 334 

6 

55 

768348 

2-90 

908416 

i -53 

869932 

4-43 

140068 

5 

56 

768622 

2-90 

908324 

i -53 

860198 

4-43 

139802 

4 

5 7 

768697 

2-90 

908233 

i -53 

860464 

4-43 

i 3 g 536 

3 

58 

768871 

2-90 

908 1 4 1 

i -53 

860730 

4-43 

139270 

2 

5 9 

769045 

2-90 

908049 

i -53 

860996 

4-43 

139005 

1 

60 

769219 

2-90 

907958 

1 -53 

861261 

4 - 43 

138739 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(54 DEGREES.) 

















































54 (36 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

1 

2 

3 

4 

5 

6 

7 i 

8 ! 
9 

10 j 

11 

12 

1 3 

1 4 

1 5 

16 

n 

18 

*9 

20 

21 

22 

23 

24 

25 

26 

ll 

ll 

3 1 

32 

33 

34 

35 

36 

37 

38 

3 9 

4 0 

4 1 

42 

43 

44 

45 

46 

47 

48 

ft 

5 1 

52 

53 

54 
! 55 

1 56 

si 

59 

60 

9-769219 

769393 

769566 

769740 

769913 

770087 

770260 

770433 

770606 

770779 

770952 

9-771125 

771298 

771470 

77 i 6 43 

771815 

771987 

772159 

77233 i 

7725 o 3 

772675 

9-772847 

773018 

773190 

77336 i 

773533 

773704 

773875 

774046 

774217 

774388 

9-774558 

774729 

774899 

775070 

775240 

775410 

77558 o 

775750 

776920 

776090 

9-776259 

776429 

776598 

776768 

776937 

777106 

777275 

777444 

777613 

77778 i 

9-777950 

778119 

778287 

778455 

778624 

778792 

778960 

779128 

779295 

779463 

2-90 

Q .89 
2-89 
2-89 
2-89 
2-89 
2-88 
2-88 
2-88 
2-88 
2-88 

2-88 

2-87 

2-87 

2-87 

2-87 

2-87 

2-87 

2-86 

2-86 

2-86 

2-86 

2-86 

2-86 

2-85 

2-85 

2-85 

2-85 

2-85 

2-85 

2-84 

2-84 

2-84 

2-84 

2-84 

2-84 

2-83 

2-83 

2-83 

2-83 

2-83 

2-83 

2-82 

2-82 

2-82 

2-82 

2-82 

2 • 81 

2 • 81 

2 • 81 

2 • 81 

2-8i 

2 • 81 

2 • 80 

2-80 

2 • 80 

2 • 80 
2-80 

2 • 80 
2-79 
2-79 

9-907958 

907866 

907774 

907682 

907590 

907498 

907406 

907314 

907222 

907129 

907037 

9-906945 

906852 

906760 

906667 

906675 

906482 

906389 

906296 

906204 

906m 

9-906018 

906926 

905832 

905739 

905645 

905552 

9 o 5459 

9 o 5366 

905272 

905179 

9 - 9 o 5 o 85 

904992 

904898 
904804 
9047 11 
904617 
904523 
904429 
904335 
904241 

9 - 904 I 47 

9 o 4 o 53 

903959 

903864 

903770 

903676 

9 o 358 i 

908487 

903392 

903298 

9 - 9 o 32 o 3 

9 o 3 io 8 

9 o 3 oi 4 

902919 

902824 

902729 

902634 

902539 

902444 

902349 

1-53 

i -53 

i -53 

i -53 

i -53 

i -53 

1 -53 

1 -54 
x -54 
. 1-54 

1 -54 

1 -54 
i -54 

1 -64 

1 -54 
i -54 
i -54 
i -55 
i -55 
i -55 
1-55 

i -55 

1 -55 
i -55 

1 -55 

1 -55 
i -55 
i -55 

1 -56 
i -56 
i -56 

i -56 

i -56 

i -56 

i -56 

i -56 

i -56 

i -56 

1 -57 

1 -67 

1 -67 

1 - 5 -] 
i -5 7 

1 -57 

1 • 67 

1 -57 

1 -67 
i- 5 7 

1 -57 
i -58 
i -58 

i -58 

i -58 

i -58 

i -58 

i -58 

i -58 

i -58 

1*59 

1 -69 

1 -59 

9-861261 

861627 

861792 

862008 

862323 

862689 

862854 

863 u 9 
863385 
86365 o 
8639 i 5 

9-864180 

864445 

864710 

864975 

865240 

8655 o 5 

865770 

866 o 35 

8663 oo 

866564 

9-866829 

867094 

867358 

867623 

867887 

868 i 52 

868416 

868680 

868945 

869209 

9 • 869473 
869737 
870001 
870265 
870529 
870793 
871057 
871321 
87 i 585 
871849 

9-872112 

872376 

872640 

872903 

873167 

873430 

873694 

873907 

874220 

874484 

9-874747 

875010 

875273 

8 7 5536 

875800 

876063 

876326 

876689 

876851 

877114 

4-43 

4-43 

4-42 

4-42 

4-42 

4-42 

4-42 

4-42 

4-42 

4-42 

4-42 

4-42 

4.42 

4-42 

4 - 4 x 

4 - 4 i 

4 - 4 i 

4 - 4 i 

4 - 4 i 

4 - 4 i 

4 - 4 i 

4 - 4 i 

4 - 4 i 

4 - 4 i 

4 - 4 i 

4 - 4 i 

4 - 4 o 
4 - 4 o 
4 - 4 o 
4 - 4 o 
4 - 4 o 

4 - 4 o 

4.4° 

4 - 4 o 

4.40 

4-40 

4.40 

4 - 4 o 

4.40 

4.40 

4-39 

4-39 

4-39 

4-39 

4-39 

4-89 

4 - 3 9 

4-39 

4-39 

4-39 

4.39 

4*39 

4-38 

4-38 

4-38 

1 4-38 
4-38 
4-38 
4-38 
4-38 

10-138739 

138473 

138208 

137942 

137677 

137411 
137-146 

1 3688 1 

1 366 1 5 
i 3635 o 
i 36 o 85 

10 -135820 
135555 
135290 
i 35 o 25 
134760 
134495 
i 3423 o 

133965 

133700 

133436 

10-133171 

132906 
132642 
132377 
i 32 ii 3 
131848 
13 1 584 
i 3 i 32 o 
i 3 io 55 

130794 

io- i3o527 
i 3 o 263 

129999 
129735 
129471 
129207 
128943 
128679 
128416 

1 281 5 i 

10-127888 

127624 

127360 

127097 

126833 

126570 

1 263 o 6 
126043 
125780 

1 255 16 

10-125253 

124990 

124727 

124464 

124200 
123937 
123674 
123411 
123149 
122886 

60 

I? 

5 7 

56 

55 

54 

53 

52 

5 i 

5 o 

49 

48 

47 

46 

45 

44 

43 

42 

4 i 

4 o 

3 9 

38 

37 

36 

35 

34 

33 

32 

3 i 

3 o 

3 

27 

26 

25 

24 

23 

22 

21 

20 

10 
l8 

17 

l6 

i 5 

i 4 

i 3 

12 

11 

10 

7 

6 

5 

4 

3 

2 

1 

0 


Cosine 

D. 

Sine 

D. 

Tang. 

--i— 1 

D. 

Cotang. 

1 M. 


(53 DEGREES.) 




































































SINES AND TANGENTS. (37 DEGREES.) 


55 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 1 

0 

9-779463 

2-79 

9-902349 

1*59 

9-877114 

4-38 

1 

779631 

2-79 

902253 

1 -69 

877377 

4-38 

2 

779798 

2-79 

902158 

1 -59 

877640 

4-38 

3 

779966 

2-79 

902063 

1 -59 

877903 

4-38 | 

4 

78 oi 33 

2-79 

• 901967 

1 -59 

878165 

4-38 

5 

78 o 3 oo 

2-78 

901872 

1 -69 

878428 

4-38 

6 

780467 

2-78 

901776 

1 -69 

878691 

4-38 

7 

780634 

• 2-78 

901681 

1-59 

878953 

4-37 

8 

780801 

2-78 

901685 

i- 5 9 

879216 

4-37 

9 

780968 

2-78 

901490 

1 -09 

879478 

4-37 

10 

781134 

2-78 

901394 

1 -6o 

879741 

4-37 

11 

9 - 78 i 3 oi 

2-77 

9-901298 

1 -6o 

9-88ooo3 

4-37 

12 

781468 

2-77 

901202 

1 -6o 

880265 

4-37 

i 3 

781634 

2-77 

901106 

1 -6o 

880528 

4-37 

14 

781800 

2-77 

901010 

1 -6o 

880790 

4-37 

i 5 

781966 

2-77 

900914 

1 -6o 

881062 

4-37 

16 

782132 

2-77 

900818 

1 -6o 

881 3 14 

4-37 

*7 

782298 

2-76 

900722 

1 -6o 

881576 

4-37 

18 

782464 

2-76 

900626 

1 -6o 

881889 

4-37 

*9 

782630 

2-76 

900529 

1 -6o 

882101 

4-37 

20 

782796 

2-76 

900438 

1 • 61 

882363 

4-36 

21 

9-782961 

2-76 

9-900337 

1 -6i 

9-882625 

4-36 

22 

783127 

2-76 

900240 

1 • 61 

882887 

4-36 

23 

783292 

2-75 

900144 

1 -6i 

883148 

4-36 

24 

783408 

2-75 

900047 

1 -6i 

883410 

4-36 

25 

783623 

2-75 

899951 

1 -6i 

883672 

4-36 

26 

783788 

2-76 

899864 

1 • 61 

883 9 34 

4-36 

27 

783953 

2-75 

899757 

1 -6i 

884196 

4-36 

28 

784118 

2-75 

899660 

1 -6i 

884407 

4-36 

29 

784282 

2-74 

899664 

1 • 61 

884719 

4-36 

3 o 

784447 

2-74 

899467 

1-62 

884980 

4-36 

3 i 

9-784612 

2-74 

9-899370 

1 -62 

9-885242 

4-36 

32 

784778 

2-74 

89927 3 

1-62 

8 S 55 o 3 

4-36 

33 

784941 

2-74 

899176 

1 -62 

885766 

4-36 

34 

785 io 5 

2-74 

899078 

1-62 

886026 

4-36 

35 

785269 

2-73 

898981 

1-62 

886288 

4-36 

36 

785433 

2-73 

898884 

1 -62 

886549 

4-35 

37 

785597 

2-73 

898787 

1 -62 

886810 

4-35 

38 

785761 

2-73 

898689 

1-62 

887072 

4-35 

3 9 

786925 

2-73 

898692 

1 -62 

887333 

4-35 

40 

786089 

2-73 

898494 

1 -63 

887694 

4-35 

41 

9-786252 

.2-72 

9-898397 

i -63 

9-887855 

4-35 

42 

786416 

2-72 

898299 

i -63 

888116 

4-35 

43 

786579 

2-72 

898202 

i -63 

888377 

4-35 

44 

786742 

2-72 

898104 

i -63 

88863 9 

4-35 

45 

786906 

2-72 

898006 

i -63 

888900 

4-35 

46 

787069 

2-72 

897908 

i -63 

889160 

4-35 

47 

787232 

2-71 

897810 

i -63 

889421 

4-35 

48 

787395 

2-71 

897712 

1-63 

889682 

4-35 

49 

787507 

2-71 

8976i 4 

i -63 

889943 

4-35 

5 o 

787720 

2-71 

897516 

i -63 

890204 

4-34 

5 i 

9-787883 

2-71 

9-897418 

1 -64 

9-890465 

4-34 

52 

788045 

2-71 

897320 

1 -64 

890725 

4*34 

53 

788208 

2-71 

897222 

1 -64 

890986 

4-34 

54 

788370 

2-70 

897123 

1 -64 

891247 

4-34 

55 

788532 

2-70 

897025 

1 -64 

891607 

4-34 

56 

788694 

2-70 

896926 

1 -64 

891768 

4-34 

57 

7 88856 

2-70 

896828 

1 -64 

892028 

4-34 

58 

789018 

2-70 

896729 

1 -64 

892289 

4-34 

59 

789180 

2-70 

896631 

1 -64 

892649 

4-34 

60 

789342 

2-69 

896632 

1-64 

892810 

4-34 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 


(52 DEGREES.) 


Cotang. 


10-122886 
122623 
122360 
122097 
I 2 i 835 
121672 
121309 : 
121047 
.120784 ' 

120522 

120259 

io•119997 
119735 
119472 

I 102 IO 

II 8948 

ii8686 

118424 

118161 

117899 

117687 

10-117375 
11711 3 

11 6852 

116690 

116328 

116066 

1i 58 o 4 
ii 5543 
116281 
x16020 


io-ii 4758 

114497 

U 4235 

113974 
113712 
11 345 1 
113190 
112928 
112667 
112406 


10-112145 
111884 

111623 
111 36 i 
111100 
110840 
110579 
1io 3 i 8 
110057 
109796 


10-109535 

109276 

109014 

108753 

108493 

108232 

107972 

107711 
107451 
107190 


7 

6 

5 

4 

3 

2 

1 

o 


Tan g. 


M. 


hotototototototoroto Co Co Co Co Co Co Co Co Co co ^ £>>. .fx +>•» 01 CJt C>i CJi cri cn cti C7i Oi 0 s 

O to Ui O—J COO O *-« to CoCJn 000 O -• to GJ£s C7i Qn-J COO O « nj U3 O'— J COO O ^ to Oo|n Ui OO COO O 











































56 (38 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

I 2 

i 3 

«4 

15 

16 

1 7 

18 

>9 

20 

21 

22 

23 

24 

25 

26 

27 

28 

II 

1 3 i 

32 

33 

34 

35 

36 

37 

38 

3 9 
4.0 

4 1 

42 

43 

44 

45 

46 

47 

48 

t 

5 1 

52 

53 

54 

55 

56 

57 

58 

6? 

9-789342 

789504 

789665 

789827 

789988 

790149 

790310 
79047 1 
790682 
790793 
790954 

9-79111 5 
791275 
791436 
791 5^6 
791707 

79 1 9 1 7 
792077 

792237 

792397 

792007 

9-792716 

792876 

793 o 35 

793195 

793334 

798614 

793673 

793832 

793991 

794130 

9 - 7943 o 8 

794467 

794626 

794784 

794942 

795101 

796259 

795417 

795575 

795783 

9-7 9 58 9 1 
796049 
796206 

796364 

796621 

796679 

796836 

796993 

797 i 6 o 

797307 

9.797464 

797621 

797777 

797934 

798091 

798247 

798403 

798860 

798716 

798872 

2-69 

2-69 

2-69 

2-69 

2-69 

2-69 

2-68 

2-68 

2-68 

2-68 

2-68 

2-68 

2-67 

2-67 

2-67 

2-67 

2-67 

2-67 

2-66 

2-66 

2-66 

2-66 

2-66 

2-66 

2-65 

2-65 

2-65 

2-65 

2-65 

2-65 

2-64 

2-64 

2-64 

2-64 

2-64 

2-64 

2-64 

2-63 

2-63 

2-63 

2-63 

2-63 

2-63 

2-63 

2-62 

2-62 

2-62 

2-62 

2-62 

2-61 

2-61 

2-6i 

2 • 61 
2-6i 
2-6i 
2-6x 

2 -6l 

2 • 60 

2-60 

2-60 

2-60 

9-896532 

896433 

896335 

896236 

896137 

896038 

890939 

895840 

896741 

895641 

895542 

9-895443 

895343 

896244 

895145 

895045 

894945 

894846 

894746 

894646 

894546 

9-894446 

894346 

894246 

894146 

894046 

893946 

893846 

893745 

893645 

893544 

9-893444 

893343 

893243 

893142 

893041 

892940 

892839 

892739 

892638 

892536 

9-892435 

892334 

892233 

892132 

892030 

891929 

801827 

891726 

891624 

891523 

9-891421 
891319 
891217 
891116 
891013 
890911 
890809 
890707 
890606 
890603 

1 -64 

1 -65 

1 -65 

1 -65 

1 -65 

1 -65 

1 -65 
i -65 
i -65 
i '-65 

1 -65 

i-66 

1-66 

1 -66 

1 -66 
1-66 
i-66 

1 -66 

1 -66 

1 -66 

1 -66 

1 -67 

1 -67 
1-67 
1-67 
1-67 
1-67 

1 -67 

1 -67 

1 -67 
1-67 

i-68 

i-68 

1 -68 

i-68 

1 -68 

i-68 

1 -68 

1 -68 

i-68 

i-68 

1 -69 

1 -69 

1 -69 

1 -69 

1 -69 

1 -69 

1 -69 

1 -69 

1 -69 

1 -70 

1 -70 

1 -70 

1 -70 

1 -70 

1 -70 

1 -70 
1-70 
1-70 

1 -70 
1-70 

9-892810 
893070 
8 9 333 i 
893591 
6 9 385 i* 
894111 
894371 
894632 
894892 
890162 
895412 

9-895672 
896962 
896192 
896462 
896712 
896971 
897261 

897491 

897761 

898010 

9-898270 

898560 

898789 

899049 

899308 

899568 

899827 

900086 

900346 

900605 

9-900864 
901124 
901 383 
901642 
901901 
902160 

902419 

902679 

902968 

903197 

9-903465 

903714 

903973 

904262 

904491 

904760 

905008 

906267 

905026 

905784 

9•906043 
906302 
906560 
906810 
907077 
907366 
907694 

907802 

908111 
908369 

4-34 

4-34 

4-34 

4-34 

4-34 

4-34 

4-34 

4-33 • 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4 - 3 i 

4 - 3 1 

4 - 3 1 

4 * 3 1 

4 • 3 1 
4 - 3 i 

4 - 3 1 
4 - 3 i 
4 - 3 i 
4 - 3 i 

4 * 3 1 

4 * 31 
4 - 3 i 
4 - 3 i 

4 • 3 1 
4 - 3 i 

4 - 3 1 

4 • 3 1 

4 * 3 1 
4 - 3 o 
4 - 3 o 

io-107190 

106960 

106669 
106409 
106149 

106889 

105629 

io 5368 

io 5 io 8 

104848 

104588 

10 -104328 
104068 
io 38 o 8 
io 3548 
103288 
103029 
102769 
102609 

102249 

101990 

10-101730 
101470 
101211 
100951 
100692 
100462 
100173 
099914 
099654 
099395 

10-099136 

098876 

098617 

098358 

098099 

097840 

097681 

097321 

097062 

096803 

10-096645 

096286 

096027 

095768 

095609 

096260 

09499 2 

094763 

094474 

094216 

10-093967 
093698 
093440 
093 1 8 1 
092923 
092664 

092406 
092148 
091889 

091631 

! Cosine 

D. 

Sine 

I). i Cotang. D. 

Tang. 


(51 DEGREES.) 


lowwiowwwfjww OJ CO OJ UJ CO OJ U» U> OJ OJ O^UtCjrxOiOiC^C^OOiCJiO 

o H lO c^jx Ui O-J OOsO O »-< lo OJ|N Ui O—J CCnO o h io U)^ Oi O—J COsO o h W OJjiv U\ 0"-l OCvO O^IO OJj.\ U< O'-J CCnO o 















































SINES AND TANGENTS. (39 DEGREES.) 57 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

• 

0 

9-798872 

2 -6o 

9-890603 

1 -70 

9-908369 

4-3o 

10-091631 

60 

i 

799028 

2 -6o 

890400 

1 *71 

908628 

4-3o 

091372 

5 9 

2 

799184 

2 -6o 

890298 


908886 

4-3o 

091114 

58 

3 

799339 

2-59 

890195 

1-71 

909144 

4-3o 

090856 

5 7 

4 

799495 

2-59 

890093 

1.71 

909402 

4-3o 

090698 

56 

5 

799631 

2-69 

889990 

1-71 

909660 

4-3o 

090340 

55 

6 

799806 

2-59 

880888 

i* 7 i 

900918 

4-3o 

090082 

54 

7 

799962 

2-69 

889786 

i* 7 i 

910177 

4-3o 

089823 

53 

8 

800117 

2 *59 

889682 

1-71 

910435 

4-3o 

089665 

5 a 

9 

800272 

2-58 

889679 

i- 7 * 

910693 

4-3o 

089307 

5 1 

10 

800427 

2-58 

889477 

I-7 1 

9.10951 

4-3o 

089049 

5 o 

11 

9-800682 

2-58 

9-889874 

1 -72 

9-911209 

4-3o 

10-088791 

49 

12 

800737 

2-58 

889271 

1 -72 

911467 

4-3o 

o 88533 

48 

i 3 

800892 

2-58 

889168 

1-72 

911724 

4-3o 

088276 

47 

14 

801047 

2-58 

889064 

1-72 

911982 

4-3o 

088018 

46 

i 5 

801201 

2-58 

888961 

1 -72 

912240 

4-3o 

087760 

45 

16 

801 356 

2-67 

888858 

1 -72 

912498 

4-3o 

087502 

44 

*7 

8oi5ii 

2-57 

888755 

1-72 

912766 

4-3o 

087244 

43 

18 

801 665 

2-67 

88865 1 

1-72 

9i3oi4 

4-29 

086986 

42 

*9 

801819 

2-67 

888548 

1 -72 

913271 

4-29 

086729 

4 i 

20 

80197 3 

2A7 

888444 

1-73 

913529 

4-29 

086471 

4 o 

21 

9.802128 

2-57 

9 -888341 

1-73 

9-913787 

4-29 

io-o 862 i 3 

3 9 

22 

802282 

2-56 

888237 

i- 7 3 

9U044 

4-29 

086956 

38 

23 

802436 

2-56 

888i34 

i-73 

914302 

4-29 

085698 

37 

24 

802089 

2-56 

888 o 3 o 

i-73 

914560 

4-29 

085440 

36 

25 

802743 

2-56 

887926 

1- 7 3 

9U817 

4-29 

o 85 i 83 

35 

26 

802897 

2-56 

887822 

i-73 

916076 

4-29 

084926 

34 

2 7 

8 o 3 ooo 

2-56 

887718 

1.73 

9 i 5332 

4-29 

084668 

33 

28 

803204 

2-56 

887614 

i-73 

915590 

4-29 

084410 

32 

2 9 

8 o 335 7 

2-55 

887510 

1-73 

915847 

4-29 

o84i53 

3 i 

3 o 

8o35ii 

2-55 

887406 

1-74 

916104 

4-29 

o 838 q 6 

3 o 

31 

9-803664 

2-55 

9-887302 

1-74 

9-916362 

4-29 

io-o 83638 

29 

32 

803817 

2-55 

887198 

i-74 

916619 

4-29 

o 8338 i 

28 

33 

803970 

2-55 

887093 

i-74 

916877 

4-29 

o 83 i 23 

27 

34 

804123 

2-55 

886989 

i-74 

9171 34 

4.29 

082866 

26 

35 

804276 

2-54 

886885 

i-74 

917391 

4-29 

082609 

25 

36 

804428 

2-54 

886780 

i-74 

917648 

4.29 

082352 

24 

3 7 

804681 

2-54 

886676 

1-74 

917905 

4-29 

082096 

23 

38 

8 o 4734 

2-54 

886571 

i-74 

9181 63 

4-28 

081837 

22 

3 9 

804886 

2-54 

886466 

1-74 

918420 

4-28 

o 8 i 58 o 

21 

4 o 

8 o 5 o 39 

2-54 

886362 

i- 7 5 

918677 

4-28 

o8i323 

20 

4 r 

9-805191 

2-54 

9-886257 

i- 7 5 

9-918934 

4-28 

10-081066 


42 

8 o 5343 

2-53 

886102 

i- 7 5 

919191 

4-28 

080809 

l8 

43 

805496 

2-53 

886047 

l 7 5 

919448 

4-28 

o 8 o 552 

17 

44 

8o5647 

2-53 

886942 

i- 7 5 

919705 

4-28 

080295 

l6 

45 

805799 

2-53 

885837 

i- 7 5 

919962 

4-28 

o 8 oo 38 

i 5 

46 

806951 

2-53 

885732 

1-70 

920219 

4-28 

079781 

14 

47 

8061o 3 

2-53 

885627 

i- 7 5 

920476 

4-28 

079524 

i 3 

48 

806254 

2-53 

885522 

i- 7 5 

920733 

4-28 

079267 

12 

49 

806406 

2-52 

8854 i 6 

i- 7 5 

920990 

4-28 

079010 

11 

5 o 

806667 

2-52 

8853 11 

1 -76 

921247 

4-28 

078753 

10 

5 i 

9-806709 

2-52 

9-885205 

1-76 

9-92i5o3 

4-28 

10-078497 

9 

52 

806860 

2-52 

885 100 

1-76 

921760 

4-28 

078240 

8 

53 

807011 

2-52 

884994 

1 -76 

922017 

4-28 

077983 

7 

54 

807163 

2-52 

884889 

1 -76 

922274 

4-28 

077726 

6 

55 

807314 

2-52 

884783 

1 -76 

92253 o 

4-28 

077470 

5 

56 

807466 

2 - 5 l 

884677 

1-76 

922787 

4-28 

077213 

4 

57 

807615 

2 • 51 

884572 

1 -76 

923044 

4-28 

076966 

3 

58 

807766 

2 • 51 

884466 

1-76 

9233oo 

4-28 

076700 

2 

5 9 

807917 

2 • 5 1 

884360 

1 -76 

923557 

4-27 

076443 

1 

60 

808067 

2-5i 

884204 

1-77 

9238i3 

4-27 

076187 

0 


Cosine 

D. 

Siw- 

D. i 

Cotang. 

D. 

Tang. 

M. 


(50 DEGREES.) 














































58 (40 DEGREES.) A TABLE OF LOGARITHMIC 



Sine 

D. 

Cosine 

D. 

Tang. 

j D. 

Cotang. 


0 

9-808067 

2 - 5 i 

9-884254 

1-77 

9 - 92381 3 

4-27 

10-076187 

60 

i 

808218 

2 • 5 1 

884148 

1-77 

924070 

4-27 

075980 

5 9 

2 

8 o 8368 

2 - 5 i 

884042 

1-77 

924327 

4-27 

075673 

58 

3 

808619 

2 • 5 o 

883 9 36 

i -77 

92458.3 

4-27 

076417 

57 

4 

808669 

2 • 5 o 

883829 

1 'll 

924840 

4-27 

076160 

56 

5 

808819 

2 - 5 o 

883723 

1-77 

926096 

925302 

4-27 

074904 

55 

6 

808969 

2 - 5 o 

883617 

1.77 

4-27 

074648 

54 

7 

809119 

2 - 5 o 

8835 io 

1 ’ll 

925609 

926866 

4-27 

074391 

53 

8 

809269 

2 - 5 o 

8834 o 4 

1.77 

4-27 

074135 

52 

9 

809419 

2-49 

883297 

1.78 

926122 

4-27 

073878 

5 i 

IO 

809069 

2-49 

883191 

1-78 

926378 

4-27 

073622 

5 o 1 
1 

ii 

9-809718 

2-49 

9-883084 

1-78 

9-926684 

4-27 

10-073366 

49 

12 

i 3 

809868 

810017 

2-49 

2-49 

882977 

882871 

1-78 

1.78 

926S90 

927147 ' 

4-27 

4-27 

073110 

072853 

48 

47 

i 4 

810167 

2-49 

882764 

1 -78 

927403 

4-27 

072697 

46 

i 5 

8 io 3 i 6 

2-48 

882667 

1-78 

927659 

927915 

4-27 

072341 

45 

16 

810466 

2-48 

88255o 

1-78 

4-27 

072085 

44 

*7 

810614 

2-48 

882443 

1.78 

928171 

4-27 

071829 

071573 

43 

18 

810763 

2-48 

882336 

1 ’79 

928427 

4-27 

42 

19 

810912 

2-48 

882229 

1-79 

928683 

4-27 

071317 

4 i 

20 

811061 

2-48 

882121 

1.79 

928940 

4-27 

071060 

40 

21 

22 

9-811210 

811 358 

2-48 

2-47 

9-882014 

881907 

1-79 

1 *79 

9.929196 

929452 

4-27 

4-27 

10-070804 

070548 

39 

38 

23 

811607 

2-47 

881799 

1.79 

929708 

4-27 

070292 

37 

24 

811 655 

2-47 

881692 

1-79 

929964 

4*26 

070036 

36 

25 

811804 

2-47 

88 1584 

1-79 

930220 

4-26 

069780 

35 

26 

8119O2 

2-47 

881477 

1-79 

980475 

4-26 

069625 

34 

27 

812100 

2-47 

881369 

1-79 

930731 

4-26 

069269 

33 

28 

812248 

2-47 

881261 

1 -8o 

930987 

4-26 

069013 

068757 

32 

29 

812396 

2-46 

8811 53 

1 -8o 

931 243 

4-26 

3 i 

3 o 

812644 

2-46 

881046 

1 -8o 

9 3 1499 

4-26 

068601 

3 o 

3 i 

9-81-2692 

2-46 

9-880938 

88 o 83 o 

1 -8o 

9-931755 

4-26 

10-068245 

29 

32 

812840 

2-46 

1 -8o 

932010 

4-26 

067990 

28 

33 

812988 

2-46 

880722 

1 -8o 

982266 

4-26 

067734 

27 

34 

8131 35 

2-46 

88061 3 

1 -8o 

932622 

4-26 

067478 

26 

35 

8 i 3283 

2-46 

88 o 5 o 5 

1 -8o 

932778 

4-26 

067222 

25 

36 

8 i 343 o 

2-45 

88o3 9 7 

1 -8o 

933o33 

4-26 

066967 

24 

3 7 

813578 

2-45 

880289 

1 - 81 

983289 

933545 

4-26 

066711 

23 

38 

813725 

2-45 

880180 

i - 81 

4-26 

066455 

22 

39 

813872 

2-45 

880072 

1 -81 

9338 oo 

4-26 

066200 

21 

40 

814019 

2-45 

879963 

1 • 81 

9 34 o 56 

4-26 

o 65 9 44 

20 

41 

9-814166 

2-45 

9-879855 

1 • 81 

9 - 9343 u 

4-26 

io-o 6568 9 

1 9 

42 

81 43 1 3 

2-45 

879746 

1 • 81 

934567 

4-26 

o 65433 

IO 

43 

814460 

2-44 

879687 

1 • 81 

934823 

4-26 

065177 

17 

44 

814607 

2-44 

879529 

1 -81 

935078 

4-26 

064922 

l6 

45 

8 i 4753 

2-44 

879420 

1 -81 

935333 

4-26 

064667 

i 5 

46 

814900 

2-44 

879311 

1 - 81 

935589 

4-26 

064411 

i 4 

47 

81 5 o 46 

2-44 

879202 

1-82 

936844 

4-26 

064166 

i 3 

48 

8 i 5 i 9 3 

2-44 

879093 

878984 

878875 

1-82 

9 36 ioo 

4-26 

06,8900 

12 

49 

8 i 5339 

2-44 

1-82 

936355 

4-26 

063645 

11 

5 o 

81 5485 

2-43 

1-82 

9 366 io 

4*26 

063390 

10 

5 i 

9-81 563 1 

2-43 

9-878766 

1-82 

9 - 9 - 36 S 66 

4-25 

10•o 63 1 34 

9 

52 

815778 

2-43 

878656 

1-82 

937121 

4-25 

062879 

8 

53 

815924 

2-43 

878647 

1-82 

937376 

4-25 

062624 

7 

54 

816069 

2-43 

878438 

1 -82 

937632 

4-25 

o62368 

6 

55 

816210 

2-43 

878328 

1 -82 

937887 

4-25 

062113 

5 

56 

S1 636 i 

2-43 

878219 

i -83 

938142 

4-25 

061 858 

4 

67 

816507 

2-42 

878109 

i -83 

988398 

4-25 

061602 

3 

58 

81 6652 

2*42 

877999 

877890 

i -83 

938653 

4-25 

061347 

2 

5 q 

816798 

2-42 

i -83 

938908 

4*25 

061092 

1 

60 

816943 

2-42 

877780 

i -83 

9 3 9 i 63 

4-25 

060837 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(49 DEGREES.) 






















































SINES AND TANGENTS. (41 DEGREES.) 59 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

0-816943 

2-42 

9.877780 

i -83 

9 ’ 93 cfi 63 

4-25 

10-060837 

60 

i 

817088 

2-42 

877670 

i -83 

939418 

4-26 

060682 

69 

2 

817233 

2-42 

877360 

i -83 

939673 

4-25 

060327 

58 

3 

817379 

2-42 

877450 

i -83 

939928 

4-25 

060072 

57 

4 

817624 

2 - 4 l 

877340 

i -83 

940183 

4-26 

069817 

56 

5 

817668 

2-41 

877230 

1-84 

940438 

4-25 

069662 

55 

6 

817813 

2-41 

877120 

1-84 

940694 

4-26 

069306 

54 

7 

817938 

2-41 

877010 

1-84 

940949 

4-26 

069061 

53 

8 

8 i 8 io 3 

2-41 

876899 

1-84 

941204 

4-26 

068796 

52 

9 

818247 

2-41 

876789 

1-84 

941453 

4-25 

058542 

5 i 

10 

818392 

2-41 

876678 

1 -84 

9417U 

4-26 

068286 

5 o 

ii 

g•81 8536 

2-40 

9-876568 

1 -84 

9-941968 

4-26 

io-o 58 o 32 

49 

12 

818681 

2-40 

876457 

1-84 

942223. 

4 25 

°57777 

48 

i 3 

818823 

2-40 

876347 

1-84 

942478 

4-25 

067622 

47 

i 4 

818969 

2-40 

876236 

1 -85 

942733 

4-26 

067267 

46 

i 5 

819113 

2-40 

876125 

i -85 

942988 

4-25 

057012 

45 

16 

819257 

2-40 

876014 

i -85 

943243 

4-26 

066767 

44 

17 

819401 

2-40 

875904 

i -85 

943498 

4-25 

o 565 o 2 

43 

18 

819645 

2-39 

875793 

1 -85 

943752 

4-26 

066248 

42 

19 

819689 

2 - 3 q 

876682 

i -85 

944007 

4-23 

066993 

4 i 

20 

8 1983 2 

2-39 

876671 

i *85 

944262 

4-25 

066738 

40 

21 

9-819976 

2-39 

9-875459 

i .85 

9.944517 

4-25 

10-066483 

39 

22 

820120 

2-39 

875348 

1 -85 

944771 

4-24 

066229 

38 

23 

820263 

2-39 

876237 

1 -85 

946026 

4*24 

034974 

37 

24 

820406 

2-39 

875126 

1 -86 

943281 

4-24 

064719 

36 

25 

82o55o 

2-38 

875014 

1 -86 

945535 

4-24 

054465 

35 

26 

820693 

2-38 

874903 

i-86 

945790 

4-24 

064210 

34 

27 

820836 

2-38 

874791 

1 -86 

946045 

4-24 

053955 

33 

28 

820979 

2-38 

874680 

i-86 

946299 

4-24 

053701 

32 

29 

821122 

2-38 

874668 

1 -86 

946554 

4-24 

053446 

3 i 

3 o 

821 265 

2-38 

874406 

i-86 

946808 

4-24 

053192 

3 o 

3 i 

9-821407 

2-38 

9-874844 

i-86 

9-947063 

4-24 

10-052937 

29 

32 

82i55o 

2-38 

874232 

1-87 

9473i8 

4-24 

062682 

28 

33 

821693 

2-37 

874121 

1-87 

947372 

4-24 

052428 

27 

34 

82 i 835 

2-37 

874009 

1-87 

947826 

4-24 

062174 

26 

35 

821977 

2-37 

873896 

1-87 

948081 

4-24 

061919 

23 

3b 

822120 

2-37 

873784 

1-87 

948336 

4-24 

061664 

24 

37 

822262 

2-37 

873672 

1-87 

948690 

4-24 

061410 

23 

38 

822404 

2-37 

873560 

1-87 

948844 

4 - 24 

o 5 11 56 

22 

3 9 

822546 

2-37 

873448 

1.87 

949099 

4-24 

060901 

21 

4 o 

822688 

2-36 

873335 

1.87 

949353 

4-24 

060647 

20 

4 i 

9-822830 

2-36 

9-873223 

1-87 

9-949607 

4-24 

10-060393 

IQ 

42 

822972 

2-36 

873110 

i-88 

949862 

4-24 

o 5 oi 38 

10 

43 

823114 

2-36 

872998 

i-88 

960116 

4-24 

049884 

17 

44 

823255 

2-36 

872883 

i-88 

930370 

4-24 

049630 

16 

45 

823397 

2-36 

872772 

i-88 

960623 

4-24 

049375 

id 

46 

823539 

2-36 

872639 

i-88 

930879 

4-24 

049121 

14 

47 

823680 

2-35 

872547 

i-88 

9D11 33 

4-24 

048867 

i 3 

48 

823821 

2-35 

872434 

i -83 

951 388 

4-24 

048612 

12 

49 

823963 

2-35 

872321 

1 -88 

961642 

4-24 

048368 

11 

5 o 

824104 

2-35 

872208 

i-88 

961896 

4-24 

048104 

10 

5 i 

9-824245 

2-35 

9-872096 

1-89 

9-962160 

4-24 

10-047850 

9 

52 

824386 

2-35 

871981 

1 -89 

962405 

4-24 

047696 

8 

53 

824527 

2-35 

871868 

1 -89 

962669 

4-24 

047341 

7 

54 

824668 | 

2-34 

871755 

1 -89 

952913 

4-24 

047087 

6 

55 

824808 1 

2-34 

871641 

1 -89 

963167 

4-23 

046833 

5 

5b 

824949 I 

2-34 

871628 

1-89 

963421 

4-23 

046679 

4 

ll 

823090 1 

. 2-34 

871414 

1 -89 

963676 

4-23 

046326 

3 

58 

820280 

2-34 

871301 

1 -89 

963929 

4*23 

046071 

2 

5 9 

825371 

2-34 

871187 

1 -89 

964183 

4-23 

046817 

1 

60 

8255 i 1 

2-34 

871073 

1 -90 

964437 

4-23 

045563 

0 

L 

Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(48 DEGREES.) 

























































60 (42 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9 •8255 11 

2-34 

9-87*1073 

1.90 

9-964437 

4*23 

io-o 45563 

60 

i 

82565 i 

2-33 

870960 

1 -90 

954691 

4-23 

045309 

59 

2 

825791 

2-33 

870846 

1 -90 

964946 

4-23 

o 45 o 55 

58 

3 

826931 

2-33 

870732 

1 -90 

955200 

4-23 

044800 

57 

4 

82607 1 

2-33 

870618 

1 -90 

955464 

4-23 

044646 

56 

5 

826211 

2-33 

870604 

1 -90 

955707 

4-23 

044293 

55 

6 

82635 i 

2-33 

870390 

1 -90 

955961 

4-23 

044039 

54 

7 

826491 

2-33 

870276 

1 -90 

966215 

4-23 

043786 

53 

8 

82663 i 

2-33 

870161 

1 -90 

966469 

4-23 

o 4353 1 

52 

9 

826770 

2-32 

870047 

1-91 

966723 

4-23 

043277 

5 i 

IO 

826910 

2-32 

869933 

1-91 

936977 

4-23 

o 43 o 23 

5 o 

11 

9-827049 

2-32 

9-869818 

1-91 

9.957231 

4-23 

10*042769 

49 

12 

827189 

2-32 

809704 

1.91 

957485 

4-23 

o 425 i 5 

48 

i 3 

827328 

2-32 

869689 

1.91 

907739 

4-23 

042261 

47 

U 

827467 

2-32 

869474 

1-91 

967993 

4-23 

042007 

46 

i 5 

827606 

2-32 

86 g 36 o 

1.91 

968246 

4-23 

o 4 ! 7 5 4 

45 

16 

827745 

2-32 

869245 

1-91 

9585 oo 

4-23 

041 5 oo 

44 

17 

827884 

2 - 3 I 

869130 

1-91 

958754 

4-23 

041246 

43 

18 

828023 

2 • 3 I 

869016 

1 -92 

969008 

4-23 

040992 

42 

19 

828162 

2 - 31 

868900 

1-92 

959262 

4-23 

040788 

4 i 

20 

828301 

2 • 31 

868785 

1 -92 

939516 

4-23 

040484 

4 o 

21 

9-828439 

2 - 3 I 

9-868670 

1 -92 

9-959769 

4-23 

io-o 4 o 23 i 

3 9 

22 

828578 

2 - 3 I 

868555 

1 -92 

960023 

4-23 

039977 

38 

23 

828716 

2 • 3 I 

868440 

1 -92 

960277 

4-23 

039723 

37 

24 

828855 

2 - 3 o 

868324 

1 -92 

960681 

4-23 

039469 

36 

25 

828998 

2 - 3 o 

868209 

1 -92 

960784 

4-23 

039216 

35 

26 

829131 

2 • 3 o 

868098 

1 -92 

961038 

4-23 

038962 

34 

2 7 

829069 

2 • 3 o 

867978 

1 -93 

961291 

4-23 

038709 

33 

28 

829407 

2 • 3 o 

867862 

1 -93 

96I 54 ^ 

4-23 

o 38455 

32 

29 

829646 

2 • 3 o 

867747 

1 -93 

961799 

4-23 

038201 

3 i 

3 o 

829683 

2 - 3 o 

867631 

1-93 

962062 

4-23 

037948 

3 o 

3 i 

9-829821 

2-29 

9-867515 

1 -93 

9-962306 

4-23 

10-037694 

29 

32 

829959 

2 • 29 

867399 

1 -93 

962660 

4-23 

037440 

28 

33 

830097 

2-29 

867283 

1 -93 

962813 

4-23 

037187 

27 

34 

83 o 234 

2-29 

867167 

1 -93 

963067 

4-23 

o 36 g 38 

26 

35 

880372 

2-29 

867061 

1 -93 

963320 

4-23 

o 3668 o 

25 

36 

83 o 5 o 9 

2-29 

866935 

1-94 

963574 

4-23 

o 36426 

24 

37 

83 o 646 

2 • 29 

866819 

1 -94 

9 6382 7 

4-23 

o 36 i 73 

23 

38 

830784 

2 • 29 

866703 

1-94 

964081 

4-23 

035919 

22 

3 9 

83 og 2 1 

2-28 

866586 

1-94 

964335 

4-23 

o 35665 

21 

4 o 

83 io 58 

2-28 

866470 

i -94 

964588 

4-22 

o 354 i 2 

20 

41 

9 - S 3 1195 

2-28 

9-866353 

1-94 

9-964842 

4-22 

io-o 35 i 58 

Ip 

42 

83 1 33 2 

2-28 

866237 

1 *94 

966095 

4-22 

o 349 o 5 

l8 

43 

831469 

2 • 28 

866120 

1-94 

965349 

4-22 

o 3465 1 

H 

44 

83 1606 

2-28 

866004 

1 -95 

966602 

4-22 

034398 

l6 

45 

831742 

2-28 

865887 

1 -96 

965855 

4-22 

o 34 i 45 

i 5 

46 

83 1879 

2-28 

865770 

1 -95 

966105 

4-22 

033891 

14 

47 

83 201 5 

2-27 

865653 

1 -95 

966362 

4-22 

o 33638 

i 3 

48 

832152 

2-27 

865536 

1 -95 

966616 

4-22 

033384 

12 

49 

832288 

2-27 

8654 19 

i - 9 5 

966869 

4-22 

o 33 i 3 i 

11 

5 o 

832425 

2 • 27 

865302 

1 -95 

967128 

4-22 

032877 

10 

5 i 

9 •83256 1 

2-27 

9- 865 1 85 

1 -95 

9-967376 

4-22 

10-032624 


52 

832697 

2-27 

865 o 68 

1 -95 

967629 

4-22 

032371 

8 

53 

832833 

2-27 

864950 

1 -95 

967883 

4-22 

032117 

7 

54 

832969 

2-26 

864833 

1 -96 

968136 

4 • 22 

o 3 1864 

6 

55 

833 1o 5 

2-26 

864716 

1 -96 

968389 

4-22 

o 3 1611 

5 

56 

833241 

2-26 

864698 

1 -96 

968648 

4-22 

o 3 i 357 

4 

57 

833377 

2-26 

8644814 

1 -96 

968896 

4-22 

o 3 1104 

3 

58 

8335 i 2 

2-26 

864363 

1 -96 

969149 

4-22 

o 3 o 85 i 

2 

5 9 

833648 

2-26 

864245 

1 -96 

969408 

4-22 

o 3 o 597 

1 

60 

833783 

2-26 

864127 

1 -96 

969666 

4 - 22 

o 3 o 344 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(47 DEGREES.) 























































SINES AND TANGENTS. (43 DEGREES.) 61 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-833783 

2-26 

9-864127 

1 -96 

9-969666 

4-22 

io-o 3 o 344 

60 

i 

833919 

2-25 

864010 

1 -96 

969909 

4-22 

030091 

69 

2 

834 o 54 

2-25 

863892 

1.97 

970162 

4-22 

029838 

58 

3 

834189 

2-25 

863774 

1-97 

970416 

4-22 

029684 

67 

4 

834325 

2-25 

863656 

1-97 

970669 

4-22 

029331 

56 

5 

83446 o 

2-25 

863538 

1-97 

970922 

4-22 

029078 

55 

6 

834595 

2-25 

863419 

1-97 

971175 

4-22 

028825 

54 

7 

83473 o 

2-25 

8633 oi 

1-97 

971429 

4-22 

028571 

53 

8 

834865 

2-25 

863 1 83 

1-97 

071682 

4-22 

0283 i 8 

52 

9 

834999 

2-24 

863 064 

1-97 

971935 

4-22. 

028065 

5 i 

10 

835 i 34 

2 • 24 

862946 

1 • 98 

972188 

4-22 

027812 

5 o 

ii 

9-835269 

2-24 

9-862827 

1 -98 

9-972441 

4-22 

10-027569 

49 

12 

8354 o 3 

2-24 

862709 

1 -98 

972694 

4-22 

027306 

48 

i 3 

835538 

2-24 

862690 

1-98 

972948 

4-22 

027052 

47 

14 

835672 

2-24 

862471 

1-98 

973201 

4-22 

026799 

46 

i 5 

835807 

2-24 

862353 

1 -98 

973454 

4-22 

026546 

45 

16 

835941 

2-24 

862234 

1-98 

973707 

4-22 

020293 

44 

>7 

836075 

2-23 

862 ii 5 

1-98 

978960 

4-22 

026040 

43 

18 

836209 

2-23 

861996 

861877 

1-98 

974213 

4-22 

026787 

42 

19 

836343 

2-23 

1-98 

974466 

4-22 

025534 

4 i 

20 

836477 

2-23 

861758 

1 '99 

974719 

4-22 

025281 

4 o 

21 

9• 8366 i1 

2-23 

9-861 638 

1 -99 

9-974973 

4-22 

10-025027 

3 9 

22 

886745 

2-23 

861 5 19 

1-99 

975226 

4-22 

024774 

38 

23 

8368 7 8 

2-23 

861400 

1 -99 

97 5 479 

4-22 

024521 

37 

24 

837012 

2-22 

861280 

1-99 

975732 

4-22 

024268 

36 

25 

837146 

2-22 

861161 

i- 99 

975986 

4-22 

024015 

35 

26 

837279 

2-22 

861041 

1-99 

976238 

4-22 

023762 

34 

27 

837412 

2-22 

860922 

860802 

1-99 

976491 

4-22 

023609 

33 

28 

837646 

2-22 

1-99 

976744 

4-22 

023256 

32 

29 

837679 

2-22 

860682 

2-00 

976997 

977260 

4-22 

o 23 oo 3 

3 i 

3 o 

837812 

2-22 

86o562 

2-00 

4-22 

022760 

3 o 

3 i 

9-837945 

2-22 

9-860442 

2-00 

9-977603 

4-22 

10-022497 

29 

32 

838078 

2*21 

86 o 322 

2-00 

977756 

4-22 

022244 

28 

33 

838211 

2-21 

860202 

2-00 

978009 

4-22 

021991 

27 

34 

838344 

2-21 

860082 

2-00 

978262 

4-22 

021738 

26 

35 

838477 

2-21 

859962 

859842 

2-00 

97851 5 

4-22 

021486 

25 

36 

8386 io 

2-21 

2-00 

978768 

4-22 

021232 

24 

37 

838742 

2-21 

859721 

2-01 

979021 

4-22 

020979 

23 

38 

' 838875 

2-21 

859601 

2-01 

979274 

4-22 

020726 

22 

3 9 

839007 

2-21 

859480 

2-01 

979627 

4-22 

020473 

21 

40 

839140 

2-20 

859360 

2-01 

979780 

4-22 

020220 

20 

4 i 

9-839272 

2-20 

9-859239 

2-01 

9-980033 

4-22 

10-019967 

1 0 

42 

839404 

2-20 

869119 

2-01 

980286 

4-22 

OI9714 

18 

43 

83 9 536 

2 • 20 

858998 

858877 

2-01 

980538 

4-22 

019462 

17 

44 

839668 

2-20 

2-01 

980791 

4-21 

OI9209 

018956 

l6 

45 

839800 

2-20 

858756 

2-02 

981044 

4-21 

i 5 

46 

839932 

2-20 

858635 

-02 

981297 

4-21 

018703 

1 4 

47 

840064 

2-19 

8585 14 

2-02 

98 i 55 o 

4-21 

Ol 845 o 

i 3 

48 

840196 

2- 19 

8583 9 3 

2-02 

981803 

4-21 

018197 

12 

49 

840328 

2-19 

858272 

2-02 

982056 

4-21 

017944 

11 

5 o 

840459 

2 • 19 

858 i 5 i 

2-02 

982309 

4-21 

OI769I 

10 

5 1 

52 

9-840591 

840722 

2-19 

2-19 

9-858029 

857908 

2-02 

2-02 

9-982562 

982814 

4-21 

4-21 

10-017438 

017186 

2 

53 

840854 

2 -I 9 

857786 

2-02 

983067 

4-21 

016933 

7 

54 

840985 

2-19 

857665 

2-03 

983320 

4-21 

016680 

6 

55 

841116 
841247 

2- l8 

857543 

2 • o 3 

983573 

4-21 

016427 

5 

56 

2 • 18 

857422 

2 • o 3 

983826 

4-21 

016174 

4 

57 

S41378 

2- l8 

857300 

2 -o 3 

984079 

4*21 

016921 

3 

58 

84009 

2 • l8 

857178 

2 -o 3 

98433 i 

4-21 

015669 

2 

59 

841640 

2 • l8 

857056 

2 -o 3 

984584 

4-21 

oi 54 i 6 

1 

60 

841771 

2- l8 

866934 

2 -o 3 

984837 

4-21 

01 5 1 63 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(46 DEGREES.) 











































62 


(44 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9-841771 

2 

18 

9-866934 

2 

o 3 

9-984837 

4-21 

10•01 5 1 63 

60 

i 

841902 

2 

18 

856812 

2 

o 3 

985090 

4-21 

014910 

59 

2 

842033 

2 

18 

856690 

2 

04 

985343 

4-21 

014667 

58 

3 

842163 

2 

17 

856568 

2 

04 

985096 

4-21 

014404 

5 7 

4 

842294 

2 

17 

856446 

2 

04 

986848 

4-21 

oi 4 i 52 

56 

5 

842424 

2 

17 

856323 

2 

04 

986101 

4-21 

013899 

55 

6 

842555 

2 

n 

856201 

2 

04 

986354 

4-21 

013646 

54 

7 

842686 

2 

17 

856078 

2 

04 

986607 

4-21 

oiOJgJ 

53 

8 

842815 

2 

17 

855956 

2 

04 

986860 

4-21 

01 3 140 

52 

9 

842946 

2 

17 

855833 

2 

04 

-987112 

4-21 

012888 

5 i 

IO 

843076 

2 

17 

855711 

2 

o 5 

987365 

4-21 

012635 

5 o 

11 

9-843206 

2 

16 

9-855588 

2 

o 5 

9-987618 

4-21 

IO-OI 2382 

49 

12 

843336 

2 

16 

855465 

2 

c 5 

987871 

4-21 

012129 

48 

i 3 

843466 

2 

16 

855342 

2 

o 5 

988123 

4-21 

011877 

47 

14 

843595 

2 

16 

855219 

2 

o 5 

988376 

4-21 

011624 

46 

i 5 

843725 

2 

16 

855096 

2 

o 5 

988629 

4-21 

011371 

46 

16 

8^3855 

2 

16 

864073 

2 

o 5 

988882 

4-21 

011118 

44 

17 

843984 

2 

16 

854 o 5 o 

2 

o 5 

989134 

4-21 

010866 

43 

18 

844114 

2 

i 5 

854727 

2 

06 

989387 

4-21 

oio 6 i 3 

42 

19 

844243 

2 

i 5 

8546 o 3 

2 

06 

989640 

4-21 

oio 36 o 

41 

20 

844372 

2 

i 5 

854480 

2 

06 

989893 

4-21 

010107 

40 

21 

9 - 8445 o 2 

2 

i 5 

9-854356 

2 

06 

9-990145 

4-21 

10-009855 

39 

22 

84463 1 

2 

i 5 

854233 

2 

06 

99039S 

4-21 

009602 

38 

23 

844760 

2 

i 5 

864109 

2 

06 

990601 

4-21 

009349 

37 

24 

844889 

2 

i 5 

853986 

2 

06 

990903 

4-21 

009097 

36 

25 

840018 

2 

i 5 

853862 

2 

06 

991166 

4-21 

008844 

35 

26 

846147 

2 

i 5 

853738 

2 

06 

991409 

4-21 

008691 

34 

27 

846276 

2 

14 

8536 i 4 

2 

07 

991662 

4-21 

oo 8338 

33 

28 

8454 o 5 

2 

14 

853490 

2 

07 

991914 

4-21 

008086 

32 

29 

84553,3 

2 

14 

853366 

2 

07 

992167 

4-21 

007833 

3 i 

3 o 

845662 

2 

14 

853242 

2 

07 

992420 

4-21 

007580 

3 o 

3 i 

9-845790 

2 

14 

q - 853 118 

2 

07 

9-992672 

4-21 

10-007328 

29 

32 

840919 

2 

14 

852994 

2 

07 

992926 

4-21 

007075 

28 

33 

846047 

2 

14 

852869 

2 

07 

993178 

4-21 

006822 

27 

34 

846176 

2 

14 

852740 

2 

°7 

99343 o 

4-21 

006670 

26 

35 

8463 o 4 

2 

14 

852620 

2 

07 

993683 

4-21 

006317 

25 

36 

846432 

2 

i 3 

852496 

2 

08 

993936 

4-21 

006064 

24 

37 

84656 o 

2 

i 3 

852371 

2 

08 

994189 

4-21 

oo 58 i1 

23 

33 

846688 

2 

i 3 

852247 

2 

08 

994441 

4-21 

005559 

22 

39 

846816 

2 

i 3 

852122 

2 

08 

994694 

4-21 

oo 53 o 6 

21 

4 o 

846944 

2 

i 3 

85 1997 

2 

08 

994947 

4-21 

oo 5 o 53 

20 

4 i 

9-847071 

2 

i 3 

9-851872 

2 

08 

9 ' 995 1 99 

4-21 

10-004801 

IO 

42 

847' 99 - 

2 

i 3 

861747 

2 

08 

995462 

4-21 

004548 

l8 

43 

847327 

2 

i 3 

85 1622 

2 

08 

995706 

4-21 

004296 

17 

44 

847454 

2 

12 

85 1497 

2 

°9 

996957 

4-21 

004043 

l6 

45 

847582 

2 

12 

861372 

2 

°9 

996210 

4-21 

003790 

i 5 

46 

8477 0 9 

2 

12 

85 1246 

2 

°9 

996463 

4-21 

oo 3537 

14 

47 

847836 

2 

12 

85 1121 

2 

09 

996715 

4-21 

oo3285 

i 3 

48 

847964 

2 

12 

850996 

2 

°9 

996968 

4-21 

oo 3 o 32 

12 

49 

848091 

2 

12 

860870 

2 

°9 

997221 

4-21 

002779 

11 

5 o 

848218 

2 

12 

85 o 745 

2 

°9 

997473 

4-21 

002527 

10 

5 i 

9-848345 

2 

12 

9 - 85 o 6 i 9 

2 

°9 

9.997726 

4-21 

10-002274 

9 

52 

848472 

2 

11 

85 o 493 

2 

10 

997979 

4-21 

002021 

8 

53 

848699 

2 

11 

85 o 363 

2 

10 

998231 

4-21 

001769 

7 

54 

848726 

2 

11 

85 o 242 

2 

10 

998484 

4-21 

ooi 5 i 6 

6 

55 

848852 

2 

11 

85 oi16 

2 

10 

998737 

4-21 

001263 

5 

56 

848979 

2 

11 

849990 

2 

10 

998989 

4-21 

001011 

4 

5 7 

849106 

2 

11 

849864 

2 

10 

999242 

4-21 

000708 

3 

58 

849232 

2 

11 

849738 

2 

10 

999495 

4-21 

ooo 5 o 5 

2 

5 9 

849359 

2 

11 

849611 

2 

10 

999748 

4-21 

000253 

1 

60 

8494^0 

'2 

11 

849486 

2 

1 

10 

10-000000 

4-21 

10-000000 

0 

! Cosine 

D. 

Sine 

! D 


Cotang. 

! D. 

Tang. 

M. 


(45 DEGREES.) 









































A TABLE OF NATURAL SINES. 


63 



0 Deg. 

1 Deg. 

2 Deg. 

3 Deg. 

4 Deg. 


M 

S. 

c. a. 

S. 

C. 8 . 

S. 

0. s. 

S. 

C. S. 

S. 

C. S. 

M 

0 

00000 

Unit. 

01745 

99985 

03490 

99939 

o5234 

99863 

06976 

99766 

60 

i 

00029 

I-0000 

01774 

99984 

o 35 i 9 

99938 

o5263 

99861 

07006 

99754 

59 

2 

ooo 58 

I-0000 

oi 8 o 3 

99984 

o3548 

99937 

06292 

99860 

07034 

00752 

58 

3 

00087 

I *0000 

oi832 

99983 

03577 

99936 

o 532 i 

99858 

07063 

99760 

5i 

4 

00116 

1-0000 

01862 

99983 

o 36 o 6 

99935 

o 535 o 

99857 

07092 

99748 

56 

5 

ooi45 

I-0000 

01891 

99982 

o 3635 

99934 

05379 

99855 

07121 

99746 

55 

6 

00175 

I•0000 

01920 

99982 

o3664 

99933 

06408 

99854 

07160 

99744 

54 

7 

00204 

1-0000 

01949 

99981 

03693 

99932 

05437 

99852 

07179 

99742 

53 

8 

00233 

I*0000 

01978 

99980 

03723 

99931 

05466 

99861 

07208 

99740 

52 

9 

00262 

I-0000 

02007 

99980 

03752 

qqq 3 o 

o 5495 

99849 

07237 

99738 

5 i 

IO 

00291 

1.0000 

02036 

99979 

03781 

99929 

o5524 

99847 

07266 

99736 

5 o 

11 

00320 

99999 

020-5 

99979 

o 38 io 

99927 

o 5553 

99846 

07295 

99734 

49 

12 

00349 

99999 

0209.4 

99978 

o3839 

99926 

o5582 

99844 

07324 

99731 

48 

i 3 

00378 

99999 

02123 

99977 

o 3868 

99925 

o56i 1 

99 8 42 

07353 

99729 

47 

i 4 

00407 

99999 

02 I 52 

99977 

08897 

99924 

o564o 

99841 

07382 

99727 

46 

l 5 

00436 

99999 

02 l8l 

99976 

03926 

99923 

o 566 q 

99839 

07411 

99725 

45 

16 

oo«t 65 

99999 

0221 I 

99976 

o 3 g 55 

99922 

05698 

99838 

07440 

99723 

44 

17 

00495 

99999 

02240 

99975 

03984 

99921 

05727 

99836 

07469 

99721 

43 

i8 

oo524 

99999 

02269 

99974 

0401 3 

99919 

05766 

99834 

07498 

99719 

42 

19 

oo 553 

99998 

02298 

99974 

04042 

99918 

05785 

99833 

07527 

99716 

4 i 

20 

oo582 

99998 

02327 

99973 

04071 

99917 

o58i4 

99831 

07556 

99714 

4 o 

21 

00611 

99998 

02356 

99972 

04100 

99916 

o5844 

qq82q 

07585 

99712 

3 9 

22 

00640 

99998 

02385 

99972 

04129 

999 15 

06873 

99827 

07614 

99710 

38 

23 

00669 

99998 

02414 

99971 

04 i 5 g 

999 13 

05902 

99826 

07643 

99708 

3 7 

24 

00698 

99998 

02443 

99970 

04188 

999 12 

05931 

99824 

07672 

99705 

36 

25 

00727 

99997 

02472 

99969 

04217 

99911 

06960 

99822 

07701 

99703 

35 

26 

00756 

99997 

02601 

99969 

04246 

99910 

06989 

99821 

07730 

99701 

34 

27 

00785 

99997 

o253o 

9qq68 

04275 

99909 

06018 

99 8i 9 

° 7 7 5 p 

99699 

33 

28 

00814 

99997 

02660 

99967 

o 43 o 4 

99907 

06047 

99S17 

07788 

006q6 

32 

29 

00844 

9999 6 

02689 

99966 

04333 

99906 

06076 

99816 

07817 

99694 

3 i 

3 o 

00873 

99996 

02618 

99966 

04362 

99905 

o 6 io 5 

99813 

07846 

99692 

3 o 

3 i 

00902 

99996 

02647 

99965 

04391 

99904 

o 6 i 34 

99812 

07875 

99689 

29 

32 

00931 

99996 

02676 

99964 

04420 

qqq02 

061 63 

99810 

07904 

99687 

20 

33 

00960 

99995 

02705 

99963 

04449 

9990 1 

06192 

99808 

07933 

99685 

27 

34 

00989 

99995 

02734 

99963 

04478 

99900 

06221 

99806 

07962 

99683 

26 

35 

01018 

99995 

02763 

99962 

04607 

99898 

06260 

99804 

0799 1 

99680 

25 

36 

01047 

99995 

02792 

99961 

04536 

99897 

06279 

99803 

08020 

99678 

24 

37 

01076 

99994 

02821 

99960 

04565 

qq 8q6 

o 63 o 8 

99801 

08049 

99676 

23 

38 

01 io 5 

99994 

o285o 

99959 

04594 

99894 

06337 

99799 

08078 

99673 

22 

39 

on 34 

99994 

1 02879 

99969 

04623 

qq 8 q 3 

o 6366 

99797 

08107 

99671 

21 

40 

01164 

99998 

02908 

99958 

04653 

99892 

06395 

99795 

o 8 i 36 

99668 

20 

41 

01193 

99993 

02938 

99967 

04682 

99890 

064.24 

99793 

o 8 i 65 

99666 

19 

42 

01222 

99993 

02967 

99966 

04711 

9q88q 

00453 

99792 

08194 

99664 

l8 

43 

01261 

99992 

02996 

qqq 55 

o474o 

99888 

06482 

99790 

08223 

99661 

17 

44 

01280 

99992 

o3o25 

99964 

04769 

99886 

o 65 i 1 

99788 

08262 

99659 

l6 

45 

01309 

99991 

o3o54 

99953 

04798 

99885 

o 654 o 

99786 

08281 

99657 

i 5 

46 

oi 338 

99991 

o 3 o 83 

99952 

04827 

99883 

06669 

99784 

o 83 io 

99654 

14 

47 

01367 

99991 

o 3 i 12 

99952 

04856 

99882 

06598 

99782 

08339 

99652 

i 3 

48 

01396 

99990 

o 3 i 4 i 

99951 

04885 

99881 

06627 

99780 

o 8368 

99649 

12 

49 

01426 

99990 

03170 

99900 

04014 

99879 

o 6656 

99778 

08397 

99647 

11 

5 o 

01454 

99989 

03199 

99949 

04943 

99878 

06686 

99776 

08426 

99644 

10 

5 i 

0 1483 

99989 

o322o 

99948 

04972 

99876 

06714 

99774 

o 3455 

99642 

9 

52 

oi5i3 

99989 

o3257 

99947 

o 5 ooi 

99875 

06743 

99772 

08484 

99639 

8 

53 

01542 

99988 

03286 

99946 

o 5 o 3 o 

99873 

06773 

99770 

o 85 i 3 

99637 

7 

54 

0071 

qqqSS 

o 33 i 6 

99945 

o5o59 

99872 

06802 

99768 

08642 

99635 

6 

55 

01600 

99987 

o 3345 

99944 

o 5 o 88 

99870 

o 683 i 

99766 

08671 

99632 

5 

56 

01629 

99987 

o 3374 

99943 

o 5 i 17 

qq86q 

06860 

99764 

08600 

99630 

4 

57 

01 658 

q9q86 

o 34 o 3 

99942 

o5i46 

99867 

06889 

99762 

08629 

99627 

3 

58 

01687 

99986 

o3432 

99941 

06176 

99866 

06918 

99760 

o 8658 

99620 

2 

59 

01716 

99985 

03461 

99940 

o52o5 

99864 

06947 

99758 

08687 

99622 

1 

M 

C. S. 

S. 

C. S. 

s. 

C. S. 

s. 

C. S. 

S. 

C. S. 

S. 

M 


89 Deg. 

88 Deg. 

87 Deg. 

86 Deg. 

85 Deg. 































































64 A TABLE OF NATURAL SINES. 



5 Deg. 

6 Deg. 

7 Deg. 

8 Deg. 

9 Deg. 


M 

S. 1 c. s. 

S. 

C. S. 

S. 

| C. S. 

S. 

C. S. 

S. 

.0 S. 

M 

0 

08716 

: 99 6i 9 

io453 

99402 

12187 

j 99255 

*39*7 

99027 

15643 

98769 

60 

i 

08745 

99617 

10482 

99449 

12216 

99261 

13946 

99026 

15672 

98764 

5 9 

2 

08774 

99614 

1 o511 

99446 

12246 

j 99 2 48 

13976 

99019 

16701 

98760 

58 

3 

oS8o3 

99612 

10640 

99443 

12274 

99244 

14004 

99016 

16730 

98750 

57 

4 

o8S31 

qq6oq 

10669 

99440 

I 2302 

99240 

i4o33 

99011 

i5758 

98761 

56 

5 

08860 

99607 

10597 

99437 

12331 

99237 

14061 

99006 

16787 

98746 

55 

6 

08889 

99604 

10626 

99434 

1236o 

99233 

14090 

99002 

15816 

98741 

54 

7 

08918 

99602 

io655 

9943i 

12389 

99230 

14119 

98998 

16845 

98737 

53 

8 

08947 

99599 

10684 

99428 

12418 

99226 

14148 

98994 

15873 

98732 

52 

9 

08976 

99696 

10713 

99424 

12447 

99222 

14177 

98990 

15902 

98728 

5i 

IO 

09006 

99694 

10742 

99421 

12476 

99219 

14205 

98986 

i5g3i 

98723 

5o 

11 

09034 

99591 

10771 

99418 

I25o4 

99216 

14234 

98982 

109O9 

98718 

49 

12 

09063 

99688 

10800 

994i5 

12533 

99211 

14263 

98978 

15988 

98714 

48 

i3 

09092 

99686 

10829 

99412 

12562 

99208 

14292 

98973 

16017 

98709 

47 

i4 

09121 

99583 

io858 

99409 

12691 

99204 

14320 

98969 

16046 

98704 

46 

15 

09160 

99680 

10887 

99406 

12620 

99200 

14349 

98960 

16074 

98700 

40 

16 

09179 

99578 

10916 

99402 

12649 

99197 

14378 

98961 

i6io3 

$86g5 

44 

17 

09208 

9 9 5?5 

10945 

99399 

12678 

99193 

14407 

98967 

1613 2 

98690 

43 

18 

09237 

99572 

10973 

99396 

12706 

99189 

14436 

98963 

16160 

98686 

42 

x 9 

09266 

99670 

11002 

99393 

12735 

99186 

14464 

98948 

16189 

98681 

41 

20 

09296 

99567 

1 io31 

993 go 

12764 

99182 

14493 

98944 

16218 

98676 

40 

21 

09324 

99564 

11060 

99386 

12793 

99178 

14522 

98940 

16246 

98671 

39 

22 

09353 

99062 

11089 

99383 

12822 

99175 

14551 

98936 

16275 

98667 

38 

23 

09382 

99559 

11118 

99380 

12851 

99171 

14580 

98931 

163 04 

98662 

37 

24 

09411 

99556 

11147 

99377 

12880 

99167 

14608 

98927 

16333 

98667 

36 

25 

09440 

99553 

11176 

99374 

12908 

99163 

14637 

98926 

16361 

98662 

35 

26 

09469 

9955i 

I I2o5 

99370 

12987 

99160 

14666 

98919 

16390 

98648 

34 

27 

09498 

99548 

11234 

99367 

12966 

99156 

14695 

98914 

16419 

98643 

33 

28 

09627 

99645 

11263 

99364 

12995 

99152 

14723 

98910 

16447 

98638 

32 

29 

09666 

99642 

11291 

99360 

i3o24 

99148 

14762 

98906 

16476 

98633 

3i 

3o 

09686 

99540 

I 1320 

99357 

i3o53 

99144 

14781 

98902 

i65o5 

98629 

3o 

3i 

09614 

99537 

11349 

99354 

i3o8i 

99141 

14810 

98897 

16533 

98624 

29 

32 

09642 

99534 

11378 

9935i 

13110 

99*37 

14838 

98896 

16562 

98619 

28 

33 

09671 

99531 

11407 

99347 

13139 

99133 

14867 

98889 

16691 

98614 

27 

34 

09700 

99628 

11436 

99344 

13168 

99129 

14896 

98884 

16620 

98609 

26 

35 

09729 

99O26 

11465 

99341 

1 3197 

99125 

14925 

98880 

16648 

98604 

25 

36 

09768 

99623 

1 i4o4 

99337 

13226 

99122 

14964 

98876 

16677 

98600 

24 

37 

09787 

99520 

11523 

99334 

13264 

99118 

14982 

98871 

16706 

98595 

23 

38 

09816 

99617 

11552 

9933i 

13283 

99114 

15o 11 

98867 

16734 

985yo 

22 

3 9 

09845 

99614 

1 i58o 

99327 

13312 

99110 

1 5o4o 

98863 

16763 

98585 

21 

4o 

09874 

99511 

11609 

99324 

13341 

99106 

16069 

98868 

16792 

98580 

20 

4i 

09903 

99608 

11638 

99320 

13370 

99102 

15097 

98864 

16820 

98575 

19 

42 

09932 

99506 

11667 

99317 

13399 

99098 

15126 

98849 

16849 

98670 

18 

43 

09961 

99603 

11696 

99314 

13427 

99094 

15155 

98845 

16878 

9S565 

*7 

44 

0QQ90 

99600 

11725 

99310 

;Ui56 

99091 

151S4 

98841 

16906 

98561 

16 

45 

10019 

99497 

11764 

99307 

1340- 

99087 

102 12 

9 8836 

16986 

98556 

i5 

46 

10048 

99494 

11783 

993o3 

i35i4 

99083 

15241 

98832 

16964 

9855i 

14 

47 

10077 

99491 

11812 

9g3oo 

13543 

99079 

15270 

98827 

16992 

98646 

i3 

48 

10106 

99488 

11840 

99297 

13572 

99075 

15292 

98823 

17021 

98641 

12 

49 

1013 5 

99486 

11869 

99293 

i36oo 

99071 

15327 

98818 

17060 

98686 

11 

5o 

10164 

99482 

11898 

99290 

13629 

99067 

i5356 

98814 

17078 

9853i 

10 

5i 

10192 

99479 

H9 2 7 

99286 

13658 

99063 

15385 

98809 

17107 

98526 

9 

52 

10221 

99476 

11966 

99283 

13687 

99069 

154i4| 

98800 

17136 

98621 

8 

53 

I025o 

99473 

11986 

99279 

13716 

99o55 

16442 

98800 

17164 

98516 

7 

54 

10279 

99470 

12014 

99276 

13744 

99061 

16471 

98796 

i 7 i 9 3 

98511 

6 

55 

io3o8 

99467 

12043 

99272 

13773 

99047 

i55oo 

98791 

17222 

98606 

5 

56 

io337 

99464 

12071 

99269 

i38o2 

99043 

15529 

9S787 

17260 

98601 

4 

57 

1 o366 

99461 

12100 

99265 

13831 

99039 

i5557 

98782 

17279 

98496 

3 

58 

10395 

99468 

12129 

99262 

i3S6o 

99035 

15586 

98778 

i 7 3o3 

98491 

2 

5 9 

10424 

99455 

12158 

99268 

13889 99031 

1 56 1 5 

98773 

17336 

98466 

1 

M 

S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

s. 

C. S. 

S. 

M 


84 Deg. 

83 Deg. 

82 Deg. 

81 Deg. 

80 Deg. 


















































































A TABLE OF NATURAL SINES. 


65 



10 Deg. 

11 Deg. 

12 Deg. 

13 Deg. 

14 Deg. 


M 

S. 

C. S. 

S. 

0 . S. 

S. 

C. S. 

S. 

0 . S. 

S. 

0 . S. 

M 

0 

17360 

98481 

19081 

98163 

20791 

97815 

22495 

97437 

24192 

97 o 3 o 

60 

i 

17393 

98476 

19109 

98157 

20820 

97809 

22523 

9743 o 

24220 

97023 

5 9 

2 

17422 

98471 

19138 

98162 

20848 

97808 

22552 

97424 

24249 

97015 

58 

3 

i 745 i 

98466 

19167 

98146 

20877 

97797 

22680 

97417 

24277 

97008 

57 

4 

‘7479 

98461 

19195 

98140 

20905 

9779 * 

226o8 

97411 

243 o 5 

97001 

56 

5 

17008 

98455 

19224 

98135 

20933 

97734 

22637 

97404 

24333 

9699I 

55 

6 

17037 

98450 

19252 

9S129 

20962 

97773 

22665 

97398 

24362 

96987 

54 

7 

17665 

98445 

19281 

98124 

20990 

97772 

22693 

97391 

24390 

96980 

53 

8 

17094 

98440 

19309 

98118 

21019 

97766 

22722 

97-584 

24418 

96973 

52 

9 

17623 

98435 

19338 

98112 

21047 

97760 

22750 

97378 1 

24446 

96966 

5 i 

IO 

17661 

98430 

19366 

98107 

21076 

97764 

22778 

9737 * 

24474 

96 q 5 q 

5 o 

11 

17680 

98425 

19895 

98101 

21104 

97748 

22807 

97365 

245 o 3 

96952 

49 

I 2 

17708 

98420 

19423 

98096 

2 1132 

97742 

22835 

97358 

2453 i 

96945 

48 

i 3 

17737 

98414 

19452 

98090 

21161 

97735 

22863 

9735 1 

24559 

96937 

47 

i 4 

17766 

98400 

19481 

98084 

21189 

97729 

22892 

97345 

24587 

96930 

46 

i 5 

1 779-4 

98404 

19509 

98079 

21218 

97723 

22920 

97338 

24615 

96923 

45 

16 

17823 

98399 

19538 

98073 

21246 

977*7 

22948 

9733 i 

24644 

96916 

44 

17 

17852 

98394 

19666 

98067 

21275 

97711 

22977 

97325 

24672 

q6qoq 

43 

18 

17880 

9838 9 

19596 

98061 

2 i 3 o 3 

97706 

23 oo 5 

973 i 8 

24700 

96902 

42 

19 

17909 

98383 

19623 

98056 

21 33 i 

97698 

23 o 33 

973 h 

24728 

q 68 o 4 

4 i 

20 

17937 

983-78 

19652 

98 o 5 o 

2 i 36 o 

97692 

23062 

97604 

24756 

96887 

4 o 

21 

17966 

98873 

19680 

98044 

21 388 

97686 

23 ogo 

97298 

24784 

96880 

3 9 

22 

17995 

98368 

19709 

98039 

21417 

97680 

23 118 

9729 * 

248 i 3 

96873 

38 

23 

18023 

98362 

19737 

98033 

21445 

97673 

23146 

97284 

24841 

96866 

87 

24 

i 8 o 52 

98357 

19766 

98027 

21474 

97667 

23175 

97278 

24869 

96868 

36 

25 

18081 

98352 

*9794 

98021 

2 i 5 o 2 

97661 

23203 

97271 

24897 

96851 

35 

26 

18109 

98347 

19823 

98016 

2 i 53 o 

97655 

23231 

97264 

24926 

96844 

34 

27 

181 38 

98341 

19851 

98010 

21559 

97648 

23260 

97257 

24953 

96837 

33 

28 

18166 

98336 

19880 

98004 

21687 

97642 

23288 

97251 

24982 

96829 

32 

29 

i 8 i 9 5 

9833 i 

19908 

97998 

21616 

97636 

233 16 

97244 

25 oio 

96822 

3 i 

3 o 

18224 

98325 

1 99 3 7 

97992 

21644 

97 & 3 o 

23345 

97237 

25 o 38 

96815 

3 o 

3 i 

18252 

98320 

19965 

97987 

21672 

97623 

23373 

97230 

25 o 66 

96807 

20 

32 

18281 

983 1 5 

19994 

97981 

21701 

97617 

23401 

97223 

25 oq 4 

96800 

28 

33 

18309 

983 io 

20022 

97973 

21729 

97611 

23429 

97217 

25 i 22 

96793 

27 

34 

18338 

983 o 4 

2 oo 5 i 

97969 

21758 

97604 

23458 

97210 

25 1 5 1 

96786 

26 

35 

18867 

98299 

20079 

97 9 63 

21786 

97698 

23486 

97203 

25 17 q 

96778 

25 

36 

18395 

98294 

20108 

97938 

21814 

97592 

2 3 5 14 

97196 

26207 

96771 

24 

37 

18424 

98288 

2 oi 36 

97962 

21843 

97585 

23542 

97*89 

25235 

96764 

23 

38 

18452 

98283 

2 oi 65 

97946 

21871 

97579 

23571 

97182 

25263 

96756 

22 

3 g 

18481 

98277 

20193 

97940 

21890 

97573 

23599 

97*76 

25291 

96749 

21 

3 o 

18009 

98272 

20222 

97934 

21928 

97566 

23627 

97*69 

25320 

96742 

20 

4 i 

1S 538 

98267 

20260 

97928 

21966 

97660 

23656 

97162 

25348 

96734 

*9 

42 

18567 

98261 

20279 

97922 

21985 

97553 

23684 

97 i 55 

26376 

96727 

18 

43 

18695 

98256 

2 o 3 o 7 

979 16 

2201 3 

97647 

23712 

97*48 

25404 

96719 

*7 

44 

18624 

98250 

2 o 336 

979 10 

22041 

97541 

23740 

97 * 4 i 

25432 

96712 

16 

45 

18652 

98245 

2 o 364 

97 9 °5 

22070 

97634 

23769 

97*64 

25460 

96705 

i 5 

46 

18681 

98240 

20893 

97899 

22098 

97628 

23797 

97*27 

25488 

q66q7 

14 

47 

18710 

98234 

20421 

97893 

22126 

97521 

23825 

97120 

255 16 

96690 

i 3 

48 

18738 

98229 

20460 

97887 

2 21 55 

9761 5 

23853 

97**6 

25545 

96682 

12 

49 

1 8767 

98223 

20478 

97881 

22183 

975 o 8 

23882 

97106 

26673 

96675 

11 

5 o 

18795 

98218 

20607 

97875 

22212 

97502 

23910 

97100 

256 oi 

96667 

10 

5 i 

18824 

98212 

2 o 535 

97869 

22240 

97496 

23 9 38 

97098 

25629 

96660 

9 

52 

i 8852 

98207 

2 o 563 

97863 

22268 

97489 

23966 

97086 

25657 

96653 

8 

53 

18881 

98201 

20592 

97857 

22297 

97483 

23995 

97079 

25685 

96645 

7 

54 

18910 

98196 

20620 

97851 

22325 

97476 

24023 

97072 

25713 

96638 

6 

55 

i 8 9 38 

98190 

20649 

97845 

22353 

97470 

24 o 5 i 

97065 

25741 

96630 

5 

56 

18967 

98186 

20677 

97839 

22382 

97463 

24079 

97058 

25769 

96623 

4 

57 

18995 

9^*79 

20706 

97833 

22410 

97457 

24108 

97 o 5 i 

25798 

96616 

3 

58 

19024 

98174 

20734' 

97827 

22438 

9745o 

24136 

97044 

25826s 96608 

2 

59 

19052 

98168 

20763 

97821 

22467 

97444 

24164 

97037 

2 

96600 

1 

M 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. ' 

C. S. 

S. 

0. s. 

S. 

M 


79 Deg. 

78 Deg. 

77 Deg. 

76 Deg. 

75 Deg. 



























































66 


A TABLE OF NATUKAL SINES. 


I 



15 Deg. 

16 Deg. 

17 Deg. 

18 Deg. 

19 Deg. 


M 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

S.C. 

M 

0 

25882 

96593 

27664 

96126 

29237 

9563 o 

30902 

96106 

32667 

94552 

60 

i 

25910 

96585 

27592 

96118 

29265 

95622 

30929 

96097 

32584 

94642 

59 

2 

25938 

96678 

27620 

96110 

29293 

9661 3 

30967 

9 5 o 88 

32612 

94533 

58 

3 

25 q 66 

96570 

27648 

96102 

29321 

956 o 5 

80985 

96079 

82689 

94523 

57 

4 

25994 

96062 

27676 

96094 

29348 

95696 

3 lOI 2 

95070 

32667 

94614 

56 

5 

26022 

96500 

27704 

96086 

29376 

95588 

3 1040 

96061 

32694 

945 o 4 

55 

6 

26060 

96547 

27731 

96078 

29404 

95579 

3 1068 

g 5 o 52 

32722 

94496 

54 

7 

26079 

96540 

27759 

96070 

29432 

9 55 7 i 

| 31095 

96043 

32749 

94486 

53 

8 

26107 

96682 

27787 

96062 

29460 

95562 

3 11 23 

95 o 33 

32777 

94476 

52 

9 

261 3 5 

96524 

27815 

96064 

29487 

95554 

3 11 5 1 

96024 

32804 

94466 

5 i 

IO 

26163 

96517 

27843 

96046 

2951 5 

95545 

31178 

95 o 1 5 

32832 

94457 

5 o 

ii 

26191 

96609 

27871 

96087 

29643 

95536 

3 1206 

96006 

32869 

94447 

49 

12 

26219 

96502 

27899 

96029 

29571 

0528 

31233 

94997 

32887 

94438 

48 

i 3 

26247 

96494 

27927 

96021 

29599 

95519 

31261 

94988 

32914 

<54428 

47 

U 

26276 

96486 

27955 

96013 

29626 

c >55 11 

31289 

94979 

32942 

94418 

46 

i 5 

263 o 3 

96479 

27983 

96006 

29654 

955 o 2 

3 1 3 16 

94970 

32969 

94409 

45 

16 

2633 1 

96471 

28011 

96997 

29682 

95493 

3 1344 

94961 

32997 

94399 

44 

17 

26359 

96463 

28039 

95989 

29710 

95485 

3 1 3 7 

94952 

33 o 24 

94390 

43 

18 

26387 

96406 

28067 

95981 

297 3 7 

95476 

81899 

94943 

33 o 5 i 

g 438 o 

42 

19 

26415 

96448 

28095 

96972 

29765 

96467 

31427 

94933 

33079 

94370 

41 

20 

26443 

96440 

28123 

95964 

29793 

95459 

3 i 454 

94924 

33 io 6 

g 436 i 

4 o 

21 

26471 

96433 

28 i 5 o 

95966 

29821 

9545 o 

3 i 482 

94915 

33 1 34 

9435 i 

3 9 

22 

26600 

96425 

28178 

95948 

29849 

95441 

3 1 5 10 

94906 

33 161 

q 4342 

38 

23 

26528 

96417 

28206 

q 5 q 4 o 

29876 

95433 

3 1537 

94897 

33189 

94332 

37 

24 

26556 

96410 

28234 

q 5 q 3 i 

29904 

95424 

3 1 565 

94888 

332 i 6 

<54322 

36 

25 

26584 

96402 

28262 

9 5 9 23 

29932 

96416 

81593 

94878 

33244 - 

q 43 i 3 

35 

26 

26612 

96394 

28290 

9591 5 

29960 

95407 

3 i 6 2 o 

94869 

33271 

q 43 o 3 

34 

27 

26640 

96386 

283 18 

95907 

29987 

95398 

31648 

94860 

33298 

9429 3 

33 

28 

26668 

9 63 79 

28346 

95898 

3 ooi 5 

95389 

31675 

9485 i 

33326 

94284 

32 

29 

26696 

96371 

28374 

95890 

30043 

g 538 o 

31703 

94842 

33353 

94274 

3 i 

3 o 

26724 

9 6363 

28402 

9 5882 

30071 

95372 

31730 

94832 

3338 i 

94264 

3 o 

3 i 

26752 

96355 

28429 

95874 

30098 

9 5363 

3 i 758 

94823 

33408 

q 4254 

29 

32 

26780 

96347 

28457 

95865 

30126 

95354 

31786 

94814 

33436 

<54245 

23 

33 

26808 

96340 

28485 

95857 

3 oi 54 

95345 

3 181 3 

948 o 5 

33463 

q 4235 

27 

34 

26836 

96332 

285 1 3 

95849 

30182 

95337 

81841 

9479 s 

33490 

94225 

26 

35 

26864 

96824 

28541 

95841 

30209 

95328 

3 1868 

94786 

335 i 8 

94216 

25 

36 

26892 

96816 

28669 

95832 

30237 

95319 

31896 

94777 

33545 

94206 

24 

37 

26920 

96808 

28597 

95824 

30265 

953 io 

31923 

94768 

33573 

94196 

23 

38 

26948 

96301 

28625 

9 58 i 6 

30292 

953 oi 

3 1 q 5 1 

94708 

336 oo 

94186 

22 

3 9 

26976 

96298 

28652 

95807 

3 o 32 o 

95293 

3 '979 

94749 

33627 

94176 

21 

4 o 

27004 

96286 

28680 

95799 

3 o 348 

95284 

82006 

94740 

33655 

94167 

20 

4 i 

27032 

96277 

28708 

95791 

3 o 3 7 6 

95275 

32034 

9473 o 

33682 

94 i 57 

19 

42 

27060 

96269 

28736 

95782 

3 o 4 o 3 

96266 

32 o 6 i 

94721 

33710 

q 4 i 47 

l8 

43 

27088 

96261 

28764 

9 5 774 

3 o 43 1 

96257 

32089 

94712 

33737 

94 i 37 

17 

44 

27116 

96283 

28792 

95766 

30459 

95248 

32 ii 6 

94702 

33764 

94127 

l6 

45 

27144 

96246 

28820 

9 5 7 07 

3 0486 

95240 

32144 

94693 

33792 

94118 

i 5 

46 

27172 

96238 

28847 

9 5 7 49 

3 o 5 i 4 

96231 

32171 

94684 

33819 

94108 

14 

47 

27200 

96230 

28875 

95740 

3 o 542 

95222 

32199 

94674 

33846 

94098 

i 3 

48 

27228 

96222 

28903 

95732 

30070 

95213 

32227 

94665 

33874 

94088 

12 

49 

27256 

96214 

28931 

95724 

80697 

95204 

32254 

94656 

33901 

94078 

11 

5 o 

27284 

96206 

28959 

9 5 7 1 5 

30626 

95195 

32282 

94646 

33929 

94068 

10 

5 i 

27312 

96198 

28987 

90707 

3 o 653 

96186 

32309 

94637 

33 g 56 

94 o 58 

9 

52 . 

27340 

96190 

29015 

95698 

3 o 68 o 

95177 

32337 

94627 

33 9 83 

94049 

8 

53 

27368 

96182 

29042 

95690 

30708 

96168 

32364 

94618 

34 oi 1 

94039 

7 

54 

27396 

96174 

29070 

q 568 i 

30736 

96159 

32392 

94609 

34 o 38 

94029 

6 

55 

27424 

96166 

29098 

95673 

30763 

95 i 5 o 

32419 

94699 

34 o 65 

94019 

5 

56 

27462 

96188 

29126 

96664 

30791 

95142 

32447 

94590 

34093 

94009 

4 

5 7 

27480 

961 5 o 

29164 

g 5656 

3 o 8 ig 

961 33 

32474 

94680 

34120 

93999 

3 

58 

27508 

96142 

29182 

95647 

30846 

95124 

32502 

94571 

34147 

q 3 q 8 q 

2 

5 9 

27536 

96134 

29209 

96689 

30874 

95 i 1 5 

32629 

94661 

34176 

93979 

1 

M 

C. S. 

S. 

C. S. 

S. 

0 . S. 

S. 

C. S. 

S. 

c. s. i s. 

M 


74 Deg. 

73 Deg. 

72 Deg. 

71 Deg. 

70 Deg. 




































































A TABLE OF NATURAL SINES. 


67 


• 

20 Deg. 

21 Deg. 

22 Deg. 

23 Deg. 

24 Deg. 


M 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

M 

0 

34202 

93969 

3583 7 

93358 

37461 

92718 

39073 

92060 

40674 

9 i 355 

60 

i 

34229 

Q 3 g 59 

35864 

93348 

3748S 

92707 

39100 

92039 

40700 

9 i 343 

5 9 

2 

34267 

93949 

35891 

93337 

37616 

92697 

39127 

92028 

40727 

9 i 33 1 

58 

3 

34284 

93939 

36918 

93327 

37042 

92686 

39153 

92016 

40753 

91319 

57 

4 

343 11 

93929 

35945 

933i6 

37669 

92676 

39180 

92005 

40780 

91307 

56 

5 

34339 

93919 

35973 

933 o 6 

37596 

92664 

39207 

91994 

40806 

91296 

55 

6 

34366 

q 3 go 9 

36ooo 

93290 

37022 

92653 

89284 

91982 

40833 

91283 

541 

7 

34393 

93899 

36027 

93285 

37649 

92642 

39260 

9 * 97 i 

40860 

91272 

53 

8 

34421 

93889 

36o54 

93274 

37676 

92631 

39287 

9*9 5 9l 

■40886 

91260 

62! 

9 

34448 

93879 

36o8i 

93264 

37703 

92620 

39314 

91948 

40913 

91248 

5 i 

IO 

34475 

98869 

36io8 

93253 

37730 

92609 

39341 

91936 

40939 

91236 

5 o 

11 

345o3 

98809 

36i 35 

93248 

37707 

92698 

39367 

91926 

40966 

91224 

49 

12 

3453o 

93849 

36162 

93232 

37784 

92587 

39394 

919U 

40992 

91212 

48 

i 3 

34557 

98889 

36190 

93222 

37611 

92576 

3942 1 

91902 

41019 

91200 

47 

i 4 

34584 

98829 

36217 

93211 

37838 

92565 

89448 

91891 

41045 

91188 

46 

i 5 

34612 

9 3819 

36244 

93201 

37865 

92554 

39474 

9 i8 79 

41072 

91176 

45 

16 

34639 

93809 

36271 

93190 

37892 

92643 

39501 

91868 

41098 

91164 

44 

17 

34666 

9 3 799 

36298 

93180 

37919 

92532 

3 g 528 

q 1 856 

41126 

91162 

43 

i8 

34694 

9 3 789 

36325 

93169 

37946 

92521 

3g555 

91845 

41161 

91140 

42 

19 

34721 

9 3 779 

36352 

93159 

37973 

92610 

39581 

9 i833 

41178 

91128 

4 i 

20 

34748 

98769 

36379 

93148 

37999 

92499 

89608 

91822 

41204 

91116 

4 o 

21 

34775 

98769 

36406 

93137 

38026 

92488 

39635 

91810 

41 23 1 

91104 

3o 

22 

348o3 

93748 

36434 

93127 

38o53 

92477 

39661 

91799 

41257 

91092 

38 

23 

3483o 

93 7 38 

36461 

93116 

38o8o 

92466 

3q688 

9*787 

41284 

91080 

37 

24 

34857 

93728 

36488 

93io6 

38107 

92455 

39715 

9*775 

4i3io 

91068 

36 

25 

34884 

93718 

365i5 

93096 

38134 

92444 

39741 

91764 

4i337 

9 io 56 

35 

26 

34912 

93708 

36542 

93084 

38161 

92432 

89768 

91762 

41363 

91044 

34 

27 

34939 

93698 

36669 

93074 

38188 

92421 

89796 

91741 

41390 

9io32 

33 

28 

34966 

93688 

86696 

93o63 

38215 

92410 

39822 

91720 

41416 

91020 

32 

29 

34993 

98677 

36623 

93o52 

38241 

9 2 399 

39848 

91718 

4i443 

91008 

3 i 

3o 

35o2i 

93667 

3665o 

93042 

38268 

9 2388 

39875 

91706 

41469 

90996 

3 o 

31 

35o48 

93657 

36677 

93o3i 

38295 

92377 

39902 

91694 

41496 

90984 

29 

32 

35o75 

93647 

36704 

93020 

38322 

92366 

89928 

9 i683 

4l522 

90972 

28 

33 

35io2 

93637 

36731 

93oio 

38349 

92355 

39966 

91671 

41549 

90960 

27 

34 

35i3o 

93626 

36 7 58 

92999 

38376 

92848 

39982 

91660 

41676 

90948 

26 

35 

35167 

93616 

36 7 85 

92988 

384o3 

92332 

4ooo8 

91648 

41602 

90986 

25 

36 

35183 

93606 

368i2 

92978 

3843o 

92321 

4oo35 

91636 

41628 

90924 

24 

37 

35211 

93596 

3683g 

92967 

38456 

92310 

40062 

91625 

4i655 

90011 

23 

38 

35239 

93585 

36867 

92966 

384^3 

92299 

40088 

91613 

41681 

90899 

22 

39 

35266 

93075 

36894 

92945 

385io 

92287 

4o 115 

91601 

41707 

90887 

21 

40 

35293 

93565 

36921 

92935 

38537 

92276 

40141 

91590 

41734 

90875 

20 

41 

35320 

93555 

36948 

92924 

38564 

92265 

40168 

91678 

41760 

90868 

IO 

42 

35347 

98044 

36975 

92913 

38691 

92204 

40195 

91666 

41787 

9085 1 

l8 

43 

35375 

93534 

37002 

92902 

38617 

92243 

40221 

9i555 

4 1 8 1 3 

90889 

*7 

44 

35402 

93524 

37029 

92892 

38644 

92231 

40248 

9i543 

41840 

90826 

l6 

45 

30429 

935i4 

37056 

92881 

38671 

92220 

40275 

91531 

41866 

90814 

i 5 

46 

35456 

935o3 

37083 

92870 

38698 

92209 

4o3oi 

91519 

41892 

90802 

14 

47 

35484 

98493 

37110 

92869 

38725 

92198 

4o328 

915o8 

41919 

90790 

i 3 

48 

355 11 

93483 

37*37 

92849 

38752 

92186 

4o355 

91496 

41945 

90778 

12 

49 

35538 

93472 

37164 

92838 

38778 

92175 

4o38i 

91484 

41972 

90766 

11 

5o 

35565 

93462 

37191 

92827 

38So5 

92164 

40408 

9147 2 

41998 

90753 

10 

5i 

35592 

93462 

37218 

92816 

38832 

92152 

4o434 

91461 

42024 

90741 

9 

52 

356i9 

93441 

37245 

92805 

38869 

92141 

4046 1 

91449' 

42o5i 

90729 

8 

53 

35647 

9343i 

37272 

92794 

38886 

92i3o 

40488 

91437 

42077 

90717 

7 

54 

35674 

93420 

37299 

92784 

38912 

92119 

4o5i4 

91425 

42104 

90704 

6 

55 

35701 

93410 

37326 

92773 

38939 

92107 

4o54i 

9UU 

42 i3o 

90692 

5 

56 

3572S 

93400 

37353 

92762 

38966 

92096 

40567 

91402 

42 1 56 

90680 

4 

57 

35 7 55 

93389 

37380 

92761 

36993 

92085 

40694 

91390 

42i83 

90668 

3 

58 

35782 

93379 

37407 

92740 

39020 

92073 

4062 1 

91378 

42209 

90655 

2 

59 

358io 

93368 

37434 

92729 

39046 

92062 

40647 

91366 

42236 

90643 

1 j 

M 

0. S. 

S. 

C. S. 

S. 

0. S. I s. 

C. S. 

S. 

C. S. 

S. 

M 


69 Deg. 

68 Deg. 

67 Deg. 

60 Deg. 

65 Deg. 

. - 


19 
































































68 


A TABLE OF NATUKAL SINES. 



25 Deg. 

26 

Deg. 

27 

Deg. 

28 Deg. 

29 Deg. 


M 

S. 

c. s. 

S. 

0 . S. 

S. 

I C. S. 

S. 

C. S. 

S. 

C. S. 

M 

o 

42262 

9063 1 

43837 

89879 

45399 

89101 

46947 

88295 

48481 

87462 

j 60 

i 

42288 

90618 

43863 

89867 

46425 

89087 

46973 

88281 

435 o 6 

87448 

5 9 

2 

423 1 5 

90606 

43889 

89854 

4545 i 

89074 

46999 

88267 

48532 

87434 


3 

4234 1 

90094 

43916 

89841 

46477 

89061 

47024 

88264 

48067 

87420 

57 

4 

42367 

90682 

43942 

89828 

455 o 3 

89048 

47060 

88240 

48583 

87406 

56 

5 

42394 

90669 

43968 

89816 

46629 

89035 

47076 

88226 

48608 

87391 

I 55 

6 

42420 

90557 

48994 

89803 

45554 

89021 

47101 

88213 

48634 

87877 

54 

7 

42446 

90645 

44020 

8 q 7 qo 

4558 o 

89008 

47127 

88199 

48669 

8 7 363 

53 

8 

42473 

90532 

44046 

89777 

456 o 6 

88 99 5 

47 i 53 

881 85 

48684 

87349 

52 

9 

42499 

90520 

44072 

89764 

45632 

88981 

47178 

88172 

48710 

8 7 33 o 

5 i 

10 

42626 

90607 

44098 

89752 

45658 

88968 

47204 

8S1 58 

48735 

87321 

5 o 

11 

42552 

90495 

44124 

8 97 3 9 

46684 

88955 

47229 

88144 

48761 

8 7 3 o 6 

49 

12 

42578 

90483 

44 1 5 1 

89726 

45710 

88942 

47255 

88 i 3 o 

48786 

87292 

48 

i 3 

42604 

90470 

44177 

8971 3 

45736 

88928 

47281 

88117 

48811 

87278 

47 

14 

4263 1 

90458 

44203 

89700 

45762 

88915 

473 o 6 

88 1 o 3 

4883 7 

87264 

46 

i 5 

42657 

90446 

44229 

89687 

46787 

88902 

47332 

88089 

48S62 

87200 

45 

16 

42683 

90433 

44255 

89674 

458 i 3 

88888 

47358 

88075 

48888 

87235 

44 

»7 

42709 

90421 

44281 

89662 

45839 

88875 

47383 

8S062 

48913 

87221 

43 

i8 

42736 

90408 

44307 

89649 

45865 

88862 

47409 

88048 

48988 

87207 

42 

19 

42762 

90396 

44333 

8963 6 

45891 

88848 

47434 

88034 

48964 

87193 

4 i 

20 

4278S 

90383 

4^359 

89623 

46917 

88835 

47460 

88020 

48989 

87178 

40 

21 

42815 

90371 

44385 

89610 

46942 

88822' 

47486 

88006 

49014 

87164 

3 9 

22 

42841 

9 o 358 

444 H 

89 5 97 

46968 

8880S 1 

475 ii 

87993 

49040 

87 i 5 o 

38 

23 

42867 

90346 

44437 

89684 

45994 

88 79 5 ; 

47537 

87979 

49065 

871 36 

37 

24 

42894 

90334 

44464 

89071 

46020 

88782 

47662 

87960 

49090 

87121 

36 

25 

42920 

90321 

44490 

89668 

46046 

88768 

47688 

87951 

49116 

87107 

35 

26 

42946 

90309 

445 i 6 

89645 

46072 

88755 

47614 

87937 

49141 

87093 

34 

27 

42972 

90296 

44542 

89632 

46097 

88741 

47639 

87923 

49166 

87079 

33 

28 

42999 

90284 

44568 

89619 

46128 

88728 

47665 

87909 

49 > 9 2 

87064 

32 

29 

43025 

90271 

44594 

89606 

46149 

88 7 i 5 

47690 

87896 

49217 

87060 

3 i 

3 o 

43 o 5 i 

90259 

44620 

89493 

46170 

88701 

47716 

87882 

49242 

87036 

3 o 

3 i 

43077 

90246 

44646 

89480 

46201 

88688 

47741 

87868 

49268 

87021 

29 

32 

43 1 04' 

90233 

44672 

89467 

46226 

88674 

47767 

87854 

49293 

87007 

28 

33 

43 i 3 o 

90221 

44698 

89464 

46252 

88661 

47798 

87840 

493.18 

86993 

27 

34 

43 1 56 

90208 

447 2 4 

89441 

46278 

88647 

47818 

87826 

49344 

86978 

26 

35 

43182 

90196 

44760 

89428 

463 o 4 

88634 

47844 

87812 

49369 

86964 

25 

36 

48209 

90183 

44776 

8941 5 

4&33o 

88620 

47869 

87798 

49394 

86949 

24 

37 

43235 

90171 

44802 

89402 

46355 

88607 

47895 

87784 

49419 

86936 

23 

38 

43261 

90168 

44828 

89889 

46381 

885 9 3 

479 20 

87770 

49445 

86921 

22 

39 

43287 

90146 

44854 

8 9 3 7 6 

46407 

8858 o 

47946 

87756 

49470 

86906 

21 

40 

433 1 3 * 

9 oi 33 

44880 

8 9 363 

46433 

88566 

4797 1 

87743 

49495 

86892 

20 

41 

43340 

90120 

44906 

89350 

46468 

88553 

47997 

87729 

49521 

86878 

IO 

42 

43366 

90108 

44932 

89337 

46484 

8853 g 

48022 

87715 

49646 

86863 

10 

43 

43392 

90095 

44968 

89324 

46610 

88526 ; 

48048 

87701 

49671 

86849 

17 

44 

43418 

90082 

44984 

89311 

46536 

885 i 2 

48073 

87687 

49596 

86834 

l6 

45 

43445 

90070 

45 oio 

89298 

4656 i 

88499 

48099 

87673 

49622 

86820 

i 5 

46 

43471 

90057 

45 o 36 

89285 

46687 

88485 

48124 

87659 

49647 

868 o 5 

14 

47 

43497 

90045 

45062 

89272 

46613 

88472 

48 i 5 o 

87645 

49672 

86791 

i 3 

48 

43523 

90032 

45 o 88 

89259 

46639 

88458 

48175 

87631 

49697 

86777 

12 

49 

48649 

90019 

45114 

89240 

46664 

88445 

48201 

87617 

49723 

86762 

1 1 

5 o 

43575 

90007 

45 1 40 

89232 

46690 

8843 i 

48226 

87603 

49748 

86748 

10 

5 i 

436 o 2 

89994 

45 166 

89210 

46716 

88417 

48252 

8 7 58 9 

49778 

86733 

9 

52 

43628 

89981 

45192 

89206 

46742 

88404 

48277 

8 7 5 7 5 

49798 

86719 

8 

53 

43654 

89968 

46218 

89193 

46767 

883 go 

483 o 3 

8 7 56 i 

49824 

86704 

7 

54 

4368 o 

89906 

45243 

89180 

46793 

88377 

48328 

87546 

49849 

86690 

6 

55 

43706 

89943 

45269 

89167 

46819 

88363 

48354 

87532 

49874 

86675 

5 

56 

43733 

89930 

45290 

89153 

46844 

88349 

48379 

8 7 5 i 8 

49899 

86661 

4 

67 

43759 

899 1 8 

45321 

89140 

46870 

88336 ! 

484 o 5 

87604 

49924 

86646 

3 

58 

43785 

89905 

45347 

89127 

46896 

88322 

48430 

87490 

49960 

86632 

2 

5 9 

438 i 1 

89892 

45373 

89114 

46921 

883 o 8 

48456 

87476 

49975 

86617 

1 

M 

c. s. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

~M 

w- 

64 Deg. 

63 Deg. 

62 Deg. 

61 Deg. 

60 Deg. 



























































































A tabIe of natural sines. 69 



80 Deg. 

31 Deg. 

32 Deg. 

83 Deg. 

31 Deg. 


M 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

M 

o 

5oooo 

866o3 

5 i 5 o 4 

80717 

62992 

84800; 

54464 

8386 7 

55919 

82904 

60 

i 

56020 

86588 

51529 

80702 

53017 

184789' 

04488 

83851 

55943 

828S7 

5 9 

2 

5oo5o 

86073 

51 004 

80687 

53o4i 

84774 

54013 

83835 

5 5 968 

82871 

58 

3 

60076 

86559 

51579 

86672 

53o66 

84759 

54537 

838 m 

55992 

82800 

57 

4 

5oioi 

86544 

51604 

80607 

53091 

84743 

54061 

83804 

56oi6 

82839 

06 

5 

5oi26 

8653o 

5162S 

85642 

53115 

84728 

54086 

83 7 38 

56o4o 

82822 

55 

6 

5o 151 

86515 

51653 

85627 

5314o 

84712 

04610 

83772 

56o64 

82806 

04 

7 

50176 

865oi 

5i6 7 8 

80612 

53164 

84697 

54635 

83 7 56 

56 088 

82790 

53 

8 

50201 

86486 

51703 

86097 

63189 

84681! 

54609 

83740 

56112 

82 77 3 

52 

9 

50227 

86471 

51728 

85582 

53214 

84666; 

54683 

83724 

56136 

82707 

5i 

IO 

50262 

86477 

5i753 

86667 

53238 

84600 

54703 

83 7 o8 

56160 

82741 

5o 

11 

50277 

86442 

51778 

8555i 

53263 

84635 

547.82 

83602 

56i84 

82724 

49 

I 2 

5o3o2 

86427 

5i8o3 

85536 

53288 

84619 

54756 

83676 

56208 

82708 

48 

i3 

50327 

864i3 

5i823 

85521 

53312 

84604 

54781 

8366o 

562,32 

82692 

47 

i4 

5o352 

86398 

5i8o2 

»855o6 

53337 

84088, 

54800 

83645 

56256 

82670 

46 

i5 

5o377 

86384 

5i8 77 

85491 

5336i 

84073 

04829 

83629 

56280 

82609 

45 

16 

5o4o3 

8636 9 

51902 

80476 

53386 

84057' 

54804 

83613 

563o5 

82643 

44 

17 

50428 

86354 

51921 

80461 

53411 

84542 

04878 

835q7 

56329 

82626 

43 

18 

5o453 

8634o 

51962 

85446 

53435 

84026' 

54902 

8358i 

56353 

82610 

42 

>9 

60478 

86320 

51977 

80431 

53460 

8.0111 

54927 

83565 

56377 

8209,3 

4i 

20 

5o5o3 

86310 

52002 

80416 

53484 

84496, 

54951 

8354q 

56 401 

82077 

4o 

2 1 

5°528j 

86295 

52026 

80401 

53009 

84480 

04970 

83533 

06420 

82561 

3 9 

22 

5o553 

86281 

52001 

85385 

53534 

84464 

04909 

83517 

06449 

82644 

38 

23 

50678 

86266 

52076 

85370 

53558 

84448' 

5oo2 4 

835oi 

06473 

82028 37 

24 

5o6o3 

86201 

52101 

85355 

53583 

84433, 

5.0048 

83485 

56497 

025] 1 

36 

20 

60628 

86237 

52 I 26 

8o34o 

53607 

84417 

00072 

83469 

56.02 i 

82490 

35 

26 

5o654 

86222 

52101 

85325 

53632 

84402 

50097 

83453 

56545 

82478 

34 

27 

50679 

86207 

52175 

85310 

53656 

84386! 

0012 

83437 

5656q 

82462 

33 

28 

50704 

86192 

52200 

80294 

53681 

84870' 

55145 

83421 

56593 

82446 

32 

29 

50729 

86178 

52225 

80279 

53700 

84355 

55169 

834oo 

56617 

•82429 

31 

3o 

50704 

86163 

52200 

80264 

03730 

84339 1 

00194 

8333 9 

06641 

82413 

3o 

3i 

50779 

86148 

52270 

80249 

53 7 54 

84324 

55218 

833 7 3 

56665 

82196 

29 

32 

5o8o4 

86133 

O2299 

85234 

03779 

843o8; 

50242 

83356 

06689 

82,3So 

28 

33 

60829 

86119 

52324 

80218 

538o4 

84292 

5.0266 

833$o 

56713 

82 363 

27 

34 

50804 

86104 

52349 

80203 

53828 

84277 

00291 

83324 

56 7 36 

82347 

26 

35 

50879 

86089 

52374 

85188 

53853 

84261 

55315 

833oS 

56760 

82,33o 

20 

36 

50904 

86074 

52399 

85 n3 

5337' 

84240, 

5533q 

83292 

56784 

8 2 31 4 

24 

37 

60929 

86009 

5242.3 

85167 

53go2 

842 3o' 

55363 

83276 

568o3 

82297 

23 

38 

00904 

86040 

52448 

80142 

5.3926 

84214' 

55388 

83260 

56832 

82281 

22 

3 9 

50979 

860 3 0 

52473 

80127 

03901 

84198; 

56412 

83244 

56856 

82264 

21 

40 

51004 

86015 

52498 

S3112 

53975 

84182' 

55 $36 

83228 

5688o 

82248 

20 

41 

61029 

86000 

02022 

86096 

54000 

84167 1 

55460 

83212 

5-6904 

82231 

«9 

42 

5io54 

80985 

52047 

85o8i 

54024 

84101] 

55484 

83i 9 5 

56928 

82214 

18 

43 

51079 

86970 

52672 

80066 

54049 

84i3o 

5.0009 

83179 

06902 

82.98 

17 

44 

51104 

80966 

52097 

80001 

64073 

84120 

55533 

83163 

56976 

82181 

l6 

45 

5i 129 

86941 

52621 

85o35 

54097 

84104 

00007 

83147 

57000 

82160 

10 

46 

51154 

85926 

52646 

86020 

64122 

84088 

55581 

83131 

57024 

82148 

14 

47 

51179 

80911 

62671 

8ooo5 

54i46 

84072; 

556o5 

83115 

57047 

8213 2 

i3 

48 

5i 204 

80896 

62696 

84989 

5417* 

84057 

5563o 

8309S 

67071 

82110 

12 

49 

51229 

85881 

52720 

84974 

64195 

84041 

55654 

83o82 

57095 

82098 

11 

5o 

51254 

80866 

52745 

84969 

54220 

84020 

55678 

83o66 

57119 

82082 

10 

5i 

51279 

85851 

52770 

84943 

54244 

84009' 

55702 

83ooo 

67143 

82060 

5 

02 

513o4 

85836 

52794 

84928 

54269 

83994 ! 

50726 

83o34 

O7167 

82048 

8 

53 

51329 

80821 

62819 

84913 

54293 

83978, 

60700 

83oi 7 

5 7i 9 . 

82032 

7 

54 

51354 

858o6 

52844 

84897 

54317 

88962; 

50770 

83ooi 

57216 

82010 

6 

55 

51379 

86792 

52869 

84882 

54342 

8,3946 

50799 

82980 

072,38 

81999 

0 

56 

51404 

85777 

52S93 

84866 

54366 

83 9 3o| 

55823 

82969 

07262 

81982 

4 

57 

61429 

80762 

52918 

S485i 

54391 

83915! 

55847 

82908 

67286 

81965 

3 

58 

5i454 

80747 

52943 

84836 

54415 

838991 

50871 

82936 

57310 

81949 

2 

69 

01479 

86732 

52967 

84820 

04440 

83883| 

55895 

82920 

57334 

81932 

1 

M 

C. S. 

S. 

C. S. 

S. 

C. S. 

s. 1 

C. S. 

s. 

c. s. 

S. 

M 


59 Deg. 

58 Deg. 

57 Deg. 

56 Deg. 

f.5 Deg. 












































































^^Jx^^^OJGjCoCoCJCOOJOJCO OJKJ KJIOfOWfOWKJfOtOMMHM 

. O CC~— 1 COM ~ OO 00-4 O cn^OJio^OsO GC^l OQ^s U)to h. O O GC-4 0^0^4^00(0 ~ O O <X-J O O^W •- 00 


70 


A TABLE OF NATURAL SINES. 


M 

35 Deg. 

35 Deg. 

37 Deg. 

88 Deg. 

39 Deg. 

S. ! C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

1 3 

14 

1 5 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

3 0 

3 1 

32 

33 

34 

35 

36 

37 

38 

3 9 

4 0 

4 1 

42 

43 

44 

45 

46 

47 

48 

P 

5 0 

5 1 

52 

53 

54 

55 

56 

u 

59 

57358 

57381 

57405 

57429 

57453 

■ tgx 

57524 

57548 

57572 

57596 

57619 

57643 

57667 

57691 

57715 

57738 

57762 

57786 

57810 

57833 

57857 

57881 

57904 

57928 

57952 

57976 

57999 

58 o 23 

58047 

58070 

58094 
58 i 18 
58 i 4 i 
58 i 65 
58 i 8 g 
58212 
58236 
68260 
58283 
583 o 7 
5833 o 
58354 
583 7 8 
58401 
58425 

58449 
58472 
58496 
585 19 
58543 
58067 
58590 

58614 

58637 
5866 1 
58684 
68708 
58 7 3 i 
58755 

81915 
81899 
81882 
81 865 
81848 
81 832 
8181 5 
81798 
81782 
81765 
81748 
81731 
81714 

81698 

81681 

81664 

81647 
81 63 1 

81614 

81597 
8 i 58 o 
81 563 
8 i 546 
8 i 53 o 
8 i 5 i 3 
81496 
8 i 479 
81462 
8 i 445 
81428 
81412 

8 i 395 
81378 
81 36 1 

81 344 
81327 

81 3 10 
81293 
81276 
81259 
81242 
81225 
81208 
81191 
81174 
81157 

81 i4o 
8 ii 23 
81106 
81089 
81072 
8 io 55 
8 io 38 
81021 

81004 

80987 

80970 

80953 

80936 

80919 

53779 

58802 

58826 

68849 

588 7 3 

58S96 

58920 

58943 

58967 

58990 

59014 

59037 

59061 

59084 

59108 

59131 

69154 

59178 

59201 

59225 

59248 

59272 

59295 

59318 

59342 

59365 

59389 

59412 

59436 

59459 

59482 

59506 

59529 

59052 

59076 

59599 

59622 

59646 

69669 

59693 

59716 

59739 

59763 

59786 

69809 

59832 

59806 
59879 
59902 
59926 
5 99 4 9 
5 997 2 
9 999 5 
60019 
60042 
6 oo 65 
60089 
60112 
6 oi 35 
601 58 

80902 

8 o 885 

80S67 

8 o 85 o 

8 o 833 

80816 

80799 

80782 

80765 

80748 

80730 

80713 

80696 

80679 

8^602 

80644 

80627 
80610 
8059! 
80576 
8 o 558 
80 54 1 
8o524 
80507 
80489 
80472 
8 o 455 
8 o 438 
80420 
8 o 4 o 3 
8 o 386 

8 o 368 

8 o 35 i 

8 o 334 

8 o 3 i 6 

80299 

80282 

80264 

80247 

8 o 23 o 

80212 

80195 

80178' 

80160 

80143 

80125 

80108 
80091 
80073 
8 oo 56 
8 oo 38 
80021 
8 ooo 3 
79986 
79968 
7990 1 

79934 

79916 

79809 

79881 

60182 

6 o 2 o 5 

60228 

6 o 25 i 

60274 

60298 
6 o 32 i 
6 o 344 
60367 
60390 
60414 
60437 
60460 
6 o 483 
6 o 5 o 6 
60529 

6 o 553 

60576 

60599 

60622 

6 o 645 

60668 

60691 

60714 

69738 

60761 

60784 

60807 

6 o 83 o 

6 o 853 

60876 

60899 
60922 
60945 
60968 
60991 
6101 5 
6 io 38 
61061 

61084 

61107 
61 i 3 o 
611 53 
61176 
61199 
61222 

61245 
61268 
61291 
61 3 14 
6 i 337 
6 i 36 o 
6 i 383 
61406 
61429 
61401 
61474 
61497 
61020 
6 i 543 

79864 

79846 

79829 

79811 

79793 

79776 

79758 

797 -D 

79723 

79706 

79688 

79671 

79653 

79630 

79618 

79600 

79583 
79560 
79 5 47 
7953 o 
79512 
79494 
79477 
79459 
79441 
79424 
79406 
79388 
79371 
79353 
79335 

79318 

79800 

79282 

79264 

79247 

79229 
79211 
79193 
79176 
791 5 S 
79140 
79122 
79105 
79087 
79069 

79 o 5 i 

79033 

79015 

78998 

78980 

78962 

78944 

78926 

78908 

78891 

78873 

78806 

78837 

78819 

61 566 
61689 
61612 
6 i 63 o 
61 658 
61681 
61704 
61726 
61749 

61772 

61795 

61818 

61841 

61864 

61837 

61909 

61932 

61955 

61978 

62001 

62024 

62046 

62069 
62092 
6211 5 
62 i 38 
62160 
62183 

62206 

62229 

6225 i 

62274 

62297 

62320 

62342 

62365 

62388 

62411 
62433 
62456 

62479 

62502 

62024 

62547 

62070 
62692 

62616 

62633 

62660 

62683 

62706 

62728 

62751 

62774 

62796 

62819 

62842 

62864 

628S7 

62909 

78801 

78783 

78765 

78747 

78729 

78711 

78694 

78676 

78658 

78640 

78622 

78604 

78586 

78568 

7855o 

78032 

785 14 
78496 
78478 
78460 
78442 
78424 
78405 
783S7 
78369 
7835 1 
7 8333 
7 83 1 5 
78297 
78279 
78261 

78243 

78225 

78206 

78188 

78170 

78152 

78134 

78116 

78098 

78079 

78061 

78043 

78025 

78007 

77988 

77970 

77902 

779 3 4 

779 l6 

77897 

77879 

77861 

77843 

77824 

77806 

77788 

77769 

77751 

77733 

S. 

62932 
62906 
62977 
63 ooo 
63022 
63 o 45 
63 o 68 
63090 
63 11 3 
63 i 3 o 
63 1 58 
63 180 
632 o 3 
63225 
6324 S 
63271 

63293 
633 16 
6333 S 
6336 1 
63383 
63406 
63428 
63401 
63473 
63496 
635 18 
6354 o 
63563 
63585 
636 oS 

6363 o 
63653 
63675 
636 9 8 
63720 
63742 
63765 
63787 
638 10 
63832 
63854 
63877 
63899 
63922 
63944 

63966 
63989 
64011 
64 o 33 
64 o 56 
64078 
64100 

64123 

64140 

64167 

64190 

64212 

64234 

64256 

77715 

77696 

77678 

77660 

77641 

77623 

77606 

77586 

77568 

7755 o 

7753 i 

77013 
77494 
77476 
77458 
77439 
77421 
77402 
77334 
77366 
77347 
77329 
77310 
77292 
77273 
77255 
77236 
77218 

77199 

77181 

77162 

77144 

77125 

77107 

77088 

77070 

77061 

77o33 

77014 

76996 

76977 

76959 

76940 

76921 

76903 

76884 

76866 

76847 

76828 

76810 

76791 

76772 

76764 

76735 

76717 

76698 

76679 

76661 

76642 

76623 

M 

C. S. 

S. 

0 . S. 

S. 

C. S. 

S. 

C«. s. 

C. S. 

S. 

54 Deg. 

53 Deg. 

52 Deg. 

51 Deg. 

50 Deg. 


JM 

6 o 

5 9 

58 

57 

56 

55 

54 

53 

52 

5 i 

5 a 

49 

48 

47 

46 

45 

44 

43 

42 

4 i 

4 o 

3 9 

38 

37 

36 

35 

34 

33 

32 

3 i 

3 o 

3 

27 

26 

25 

24 

23 

22 

21 

20 

19 

lb 

17 

l6 

i 5 

14 

i 3 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

M 

















































































A TABLE OF NATURAL SINES. 


71 


M 

40 Deg. 

41 Deg. 

42 Deg. 

43 Deg. 

44 Deg. 

M 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

0 

64279 

76604 

656o6 

76471 

66913 

743i4 

68200 

73 r 35 

69466 

71934 

60 

i 

64301 

76686 

65628 

75452 

66935 

74295 

68221 

73 ii 6 

69487 

71914 

5 9 

2 

64323 

76067 

6565o 

75433 

66966 

74276, 

68242 

73096 

69608 

71894 

58 

3 

64346 

76648 

65672 

75414 

66978 

74266 

68264 

73076 

69529 

71873 

57 

4 

64368 

7653o 

65694 

75395 

66999 

74237 

68285 

73 o 56 

69549 

71853 

56 

5 

64390 

76511 

65716 

75375 

6702 1 

74217 

683o6 

73 o 36 

69570 

71833 

55 

6 

64412 

76492 

65788 

75356 

67043 

74198 

68327 

73 oi 6 

69691 

71813 

54 

7 

64435 

76473 

65759 

75337 

67064 

74178 

68349 

72996 

69612 

71792 

53 

8 

64467 

76455 

65781 

753 i 8 

67086 

74169 

68370 

72976 

69633 

71772 

52 

9 

64479 

76436 

658o3 

76299 

67107 

74139 

68391 

72957 

69654 

7175# 

5i 

IO 

645 oi 

76417 

65825 

70280 

67129 

74120 

68412 

72937 

69675 

7 h 32 

5o 

11 

64524 

76398 

65847 

75261 

67151 

74100 

68433 

72917 

69696 

7 Hii 

49 

12 

64546 

76380 

6586 9 

75241 

67172 

74080 

68455 

72897 

69717 

71691 

48 

i3 

64568 

76361 

65891 

75222 

67194 

74061 

68476 

72877 

69737 

71671 

47 

i4 

64590 

76342 

65913 

75203 

67216 

74041 

68497 

72807 

69758 

71660 

46 

i5 

64612 

76323 

65g35 

75184 

67237 

74Q2 2 

68518 

72837 

69779 

7i63o 

45 

16 

64635 

76304 

65n56 

75 i 65 

67268 

74002 

68539 

72817 

69800 

71610 

44 

17 

64657 

76286 

66978 

75 i 46 

67280 

73983 

6856 1 

72797 

6982 1 

71590 

43 

18 

64679 

76267 

66000 

76126 

67301 

73963 

68582 

72777 

69842 

71669 

42 

19 

64701 

76248 

66022 

75107 

67323 

73944 

686o3 

72757 

69862 

71549 

4 i 

20 

64723 

76229 

66o44 

75 o 88 

67344 

73924 

68624 

72737 

69883 

71629 

40 

21 

64746 

76210 

66066 

75069 

67366 

73904 

68645 

72717 

69904 

7i5o8 

3 9 

22 

64768 

76192 

66088 

j5o5o 

67387 

7 3885 

68666 

72697 

69926 

71488 

38 

23 

6479° 

76173 

66109 

75 o 3 o 

67409 

73865 

68688 

72677 

69946 

71468 

37 

24 

64812 

76154 

66 1 3 1 

75 oi 1 

67430 

73846 

68709 

72657 

69966 

71447 

36 

25 

64834 

76 i 35 

66153 

74992 

67452 

73826 

68730 

72637 

69987 

71427 

35 

26 

64856 

76116 

66175 

74973 

67473 

73806 

68761 

72617 

70008 

71407 

34 

27 

64878 

76097 

66197 

74953 

67495 

73787 

68772 

72597 

70029 

71386 

33 

28 

64901 

76078 

66218 

74934 

67516 

73767 

68793 

72577 

70049 

71366 

32 

29 

64923 

76059 

66240 

749i5 

67538 

73747 

68814 

72007 

70070 

71345 

3 i 

3o 

64945 

76041 

66262 

74896 

67559 

73728 

68835 

72537 

70091 

713 25 

3o 

3i 

64967 

76022 

66284 

74876 

67580 

73708 

68857 

72517 

70112 

7i3o5 

29 

32 

64989 

76003 

663o6 

74857 

67602 

73688 

68878 

72497 

70132 

71284 

28 

33 

65oi 1 

75984 

66327 

74838 

67623 

73669 

68899 

72477 

7 oi 53 

71264 

27 

34 

65o33 

75965 

66349 

74818 

67645 

73649 

68920 

72457 

70174 

71243 

26 

35 

65o55 

76946 

66371 

74799 

67666 

73629 

68941 

72437 

70195 

71223 

2D 

36 

65077 

7 5o 27 

663g3 

74780 

67688 

73610 

68962 

72417 

70215 

7 I 2o3j 

24 

37 

65099 

75008 

66414 

74760 

67709 

73590 

68983 

72397 

70236 

71182 

23 

38 

65 1 2 2 

75889 

66436 

74741 

67730 

73570 

69004 

72377 

70257 

71162 

22 

39 

65 1 44 

75870 

66458 

74722 

67752 

7355 i 

69026 

72357 

70277 

71141 

21 

40 

65166 

7585 1 

66480 

74703 

67773 

7353 i 

69046 

72337 

70298 

71121 

20 

4i 

65188 

75832 

665oi 

74683 

67795 

735 ii 

69067 

72317 

70319 

71100 

19 

42 

652io 

75813 

66523 

74664 

67816 

73491 

69088 

72297 

70339 

71080 

l8 

43 

65232 

7 5 794 

66040 

74644 

67837 

73472 

69109 

72277 

7 o 36 o 

71059 

17 

44 

65254 

75775 

66566 

74625 

67859 

73462 

69130 

72257 

7 o 38 i 

71039 

l6 

45 

65276 

75766 

66588 

74606 

67880 

73432 

69161 

72236 

70401 

71019 

i 5 

46 

65298 

75738 

66610 

74586 

67901 

73412 

69172 

72216 

70422 

70998 

U 

47 

65320 

76719 

66632 

74567 

67923 

73393 

69193 

72196 

70443 

70978 

i 3 

48 

65342 

75699' 

66653 

74548 

67944 

73373 

69214 

72176 

70463 

70957 

12 

49 

65364 

75680 

66675 

74628 

67965 

73353 

69235 

72156 

70484 

70937 

11 

5o 

65386 

7566 i 

66697 

74509 

67987 

73333 

69206 

72136 

7 o 5 o 5 

70916 

10 

5i 

654o8 

70642 

66718 

74489 

68008 

733 i 4 

69277 

72116 

7 o 525 

70896 

9 

52 

6543 o 

76623 

66740 

74470 

68029 

73294 

69298 

72095 

70546 

70875 

0 

53 

65452 

75604 

66762 

7445 i 

68o5i 

73274 

69319 

72070 

70567 

70855 

7 

54 

65474 

75585 

66783 

7443 i 

68072 

73254 

69340 

72o55 

70687 

70834 


55 

65496 

75566 

668o5 

74412 

68098 

73234 

69361 

72o35 

70608 

70813 

5 

56 

655 1 8 

75547 

66827 

74392 

68115 

73 215 

69382 

72015 

70628 

70793 

4 

57 

65540 

75528 

66848 

74373 

68136 

73196 

69403 

71995 

70649 

70772 

3 

58 

65562 

75509 

66870 

74353 

68167 

73n5 

69424 

71974 

70670 

70762 

2 

5 9 

65584 

75490 

66891 

74334 

68179 

73 1 55 

69445 

71954 

70690 

70731 

1 

60 

656o6 

75471 

66913 

74314 

68200 

73135 

69466 

71934 

707 11 

70711 

0 

TTj 

c. s 7 

S. 

C. S. 

S. 

cTsT 

S. 

C. S. 

S. 

C. s. 

S. 

M 

1 

• 49 Deg. 

48 Deg. 

47 Deg. 

46 Deg. 

45 Deg. 



















































































2 


TRAVERSE TABLE. 


Distance. 

i Deg. 

\ Deg. 

t 3 o 

Q 

Distance. 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 ] 

“Too 

0.00 

1.00 

0.01 

1.00 

0.01 

1 

9 

2.00 

0.01 

2.00 

0.02 

2.00 

0.03 

O 

& 

3 

3.00 

0.01 

3.00 

0.03 

3.00 

0.04 

3 

4 

4.00 

0.02 

4.00 

0.03 

4.00 

0.05 

4 

5 . 

5.00 

0.02 

5.00 

0.04 

5.00 

0.07 

5 

G 

6.00 

0.03 

6.00 

0.05 

6.00 

0.08 

6 

7 

7.00 

0.03 

7.00 

0.06 

7.00 

0.09 

7 

* 

8.00 

0.03 

8.00 

0.07 

8.00 

0.10 

8 

9 

9.00 

0.04 

9.00 

0.08 

9.00 

0.12 

9 

10 

10.00 

0.04 

10.00 

0.09 

10.00 

0.13 j 

10 

11 

11.00 

0.05 

11 .00 

0.10 

11.00 

0.14 

11 

12 ; 

12.00 

0.05 

12.00 

0.10 

12.00 

0.16 

12 

13 

13.00 

0.06 

13.00 

0.11 

13.00 

0.17 

13 

14 ; 

14.00 

0.06 

14.00 

0.12 

14.00 

0.18 

14 

15 I 

15.00 

0.07 

15.00 

0.13 

15.00 

0.20 1 

15 

16 

16.00 

0.07 

16.00 

0.14 

16.00 

0.21 j 

16 

17 

17.00 

0.07 

17.00 

0.15 

17.00 

0.22 

17 

18 i 

18.00 

0 08 

18 00 

0.16 

18.00 

0.24 

18 

i 9 ; 

19.00 

0.08 

19.00 

0.17 

19.00 

0 . 25 

19 

20 ! 

20.00 

0.09 

20.00 

0.17 

20.00 

0.26 j 

20 

21 

21.00 

0.09 % 

2 1 .00 

0.18 

21.00 

0.27 

21 

22 | 

22.00 

0.10 

22.00 

0.19 

22.00 

0.29 

22 

23 1 

23.00 

0.10 1 

23.00 

0.20 

23.00 

0.30 

23 

24 1 

24 . GO 

0.10 ] 

24.00 

0.21 

24.00 

0.31 | 

24 

25 i 

25.00 

0 . 11 

25.00 

0.22 

25.00 

0.33 

25 

26 ' 

26.00 

0.11 

26.00 

0.23 

26.00 

0.34 

26 

27 , 

27.00 

0.12 

27.00 

0.24 

27.00 

0.35 

27 

28 

28.00 

0.12 

28.00 

0.24 

28.00 

0.37 

28 

29 

29.00 

0.13 

29.00 

0.25 j 

29.00 

0.38 

29 

30 

30.00 

0.13 

30.00 

0.26 1 

30.00 

0.39 

30 

' 31 

31.00 

0.14 

31.00 

( f . 27 

31.00 

0.41 

31 

32 

32.00 

0.14 

32.00 

0.28 

32.00 

0.42 

32 

33 

33.00 

0.14 

33.00 

0.29 

33.00 

0.43 

33 

34 

34.00 

0.15 

34.00 

0.30 

34.00 

0.45 

34 

35 

35.00 

0.15 

35.00 

0.31 

1 35.00 

0.46 

35 

36 

36.00 

0.16 

| 36.00 

0.31 

j 36.00 

0.47 

36 

37 

37.00 

0.16 

37.00 

0.32 

i 37.00 

0.18 

37 

38 

38.00 

0.17 

38.00 

0.33 

! 38.00 

0.50 

38 

39 

39.00 

0.17 

39.00 

0.34 

39.00 

0.51 

39 

40 

40.00 

0.17 

40.00 

0.35 

40.00 

0.52 

40 

41 

41 .00 

0.18 

41.00 

0.36 

| 41.00 

0.54 

41 

42 

42.00 

0.18 

42.00 

0.37 

1 42.00 

0.55 

42 

43 

43.00 

0.19 

43.00 

0.38 

43.00 

0.56 

43 

44 

44.00 

0.19 

44.00 

0.38 

44.00 

0.58 

44 

45 

45.00 

0.20 

45.00 

0.39 

1 45.00 

0.59 

45 

46 

46.00 

0.20 

46.00 

0.40 

l | 46.00 

0.60 

46 

47 

47.00 

0.21 

47.00 

0.41 

|| 47.00 

0.62 

47 

4 8 

48.00 

0.21 

48.00 

0.42 

48.00 

1 0.63 

48 

49 

49.00 

0.21 

49.00 

0.43 

I 49.00 

0.64 

49 

! <> 50 

50.00 

0.22 

50.00 

0.44 

| 50.00 

0.65 

50 

O'-4 C* 

Distance. 

Dep. 

Lat. 

Dep. 

| Lat. 

Dep. 

Lat. * 

Distance. 

891 Deg. 

89 | 

Deg. 

89 J Deg. 

1 


























































































TRAVERSE TABLE. 


3 


Distance . 

i Deg . 

1 

2 

Deg . 

1 Deg . 

— 

Distance. 

Lat . 

Dep . 

Lat . 

Dep . 

Lat . 

j Dep . 

51 

51.00 

0.22 

51.00 

0.45 

51.00 

1 0.67 

51 

52 

52.00 

1 0.23 

52.00 

0.45 

52.00 

0.68 

52 

53 

53.00 

0.23 

53.00 

0.46 

53.00 

0.69 

1 53 

' 54 

54.00 

0.24 

54.00 

0.47 

54.00 

0.71 

1 54 

55 

55.00 

! 0.24 

55.00 

0.48 

55.00 

0.72 

1 55 

5(3 

56.00 

0.24 

56.00 

0.49 

56.00 

0.73 

1 56 

57 

57.00 

0.25 

57.00 

0.50 

57.00 

0.75 

1 57 

58 

58.00 

0.25 

58.00 

0.51 

57.99 

0.76 

58 

59 

59.00 

0.26 

59.00 

0.51 

58.99 

0.77 

59 

60 

60.00 

0.26 

6 C .00 

0.52 

59.99 

0.79 

60 

61 

61.00 

0.27 

61.00 

0.53 

60.99 

0.80 

61 

62 

62.00 

0.27 

62,00 

0.54 

61.99 

0.81 

62 | 

63 

63.00 

0.27 

63.00 

0.55 

62.99 

0.82 

03 

64 

64.00 

0.28 

64.00 

0.56 

63.99 

0.84 

64 | 

65 

65.00 

0.28 

65.00 

0.57 

64.99 

0.85 

65 ; 

66 

66.00 

0.29 

66.00 

0.58 

65.99 

0.86 

I 66 

67 

67.00 

0.29 

67.00 

0.58 

66.99 

0 . S 8 

67 

68 

68.00 

0.30 

68.00 

0.59 

67.99 

0.89 

68 

69 

69.00 

0.30 

69.00 

0.60 

68.99 

0.90 

69 

70 

70.00 

0.31 

70.00 

0.61 

69.99 

0.92 

70 

71 

71.00 

0.31 

71.00 

0.62 

70.99 

0.93 

71 

72 

72.00 

0.31 

72.00 

0.63 

71.99 

0.94 

72 

73 

73.00 

0.32 

73.00 

0.64 

72.99 

0.96 

73 

74 

74.00 

0.32 

74.00 

0.65 

73.99 

0.97 

74 

75 

75.00 

0.33 

75.00 

0.65 

74.99 

0.98 

75 

76 

76.00 

0.33 

76.00 

0.66 

75.99 

0.99 

76 

77 

77.00 

0.34 

77.00 

0.67 

76.99 

1.01 

77 

78 

78.00 

0.34 

78.00 

0 . G 8 

77.99 

1.02 

78 

79 

79.00 

0.34 

79.00 

0.69 

78.99 

1.03 

79 

80 

80.00 

0.35 

80.00 

0.70 

79.99 

1.05 

80 

81 

81.00 

0.35 

81.00 

0.71 

80.99 

1.06 

81 

82 

82.00 

0.36 

82.00 

0.72 

81.99 

1.07 

82 

83 

83.00 

0.36 

83.00 

0.72 

82.99 

1.09 

83 

84 

84.00 

0.37 

84.00 

0.73 

83.99 

1.10 

84 

85 

85.00 

0.37 

85.00 

0.74 

84.99 

1.11 

85 

86 

86.00 

0.38 

86.00 

0.75 

85.99 

1.13 

86 

87 

87.00 

0.38 

87.00 

0.76 

86.99 

1.14 

87 

88 

88.00 

0.38 

88.00 

0.77 

87.99 

1.15 

88 

89 

89.00 

0.39 

89.00 

0.78 

88.99 

1.16 

89 

90 

90.00 

0.39 

90.00 

0.79 

89.99 

1.18 

90 

91 

91.00 

0.40 

91 . 00 " 

0.79 

90.99 

1.19 

91 

92 

92.00 

0.40 

92.00 

0.80 

91.99 

1.20 

92 

93 

93.00 

0.41 

93.00 

0.81 

92.99 

1.22 

93 

94 

* 94.00 

0.41 

94.00 

0.82 

93.99 

1.23 

94 

95 

95.00 

0.41 

95.00 

0.83 

94.99 

1.24 

95 

96 

96.00 

0.42 

96.00 

0.84 

95.99 

1.26 

96 

97 

97.00 

0.42 

97.00 

0.85 

96.99 

1.27 

97 

98 

98.00 

0.43 

98.00 

0.86 

97.99 

1.28 

98 

99 

99.00 

0.43 

99.00 

0.86 

98.99 

1.30 

99 

100 

100.00 

0.44 

100.00 | 

0.87 

99.99 

1.31 

100 

6 

o 

c 

Dep . 

Lat . 

Dcp . J 

Lat. 

Dep . 

Lat. 

<a 

CJ 

C 

7i 

i/i 

Q 

89 J Deg . 

i 

i 

89 * Deg . 

891 Deg . 

a 

C/5 

5 

i 




































































































4 


TRAVERSE TABLE. 


| Distance. 

* —. 

i 

1 Deg. 

IS Dog. 

H Deg. 

U Deg. 

Distance, j 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

1.00 

0.02 

1.00 

0.02 

1.00 

0.03 

1.00 

0.03 

* 

2 

2.00 

0.03 

2.00 

0.04 

2.00 

0.05 

2.00 

0.06 

?\ 

3 

3.00 

0.05 

3.00 

0.07 

3.00 

0.08 

3.00 

0.09 

3 

4 

4.00 

0.07 

4.00 

0.09 

4.00 

0.10 

4.00 

0.12 

4 

5 

5.00 

0.09 

5.00 

0.11 

5.00 

0.13 

5.00 

0.15 

5 

6 

6.00 

0.10 

6.00 

0.13 

6.00 

0.16 

6.00 

0.18 

6 

7 

7.00 

0.12 

7.00 

0.15 

7.00 

0.18 

7.00 

0.21 

7 

8 

8.00 

0.14 

8.00 

0.17 

8.00 

0.21 

8.00 

0.25 

8 

9 

9.00 

0.16 

9.00 

0.20 I 

9.00 

0.24 

9.00 

0.23 

9 

10 

10.00 

0.17. 

10.00 

0.22 

10.00 

0.26 

10.00 

0.31 

11) 

1L 

11.00 

0.19 

IT .00 

0.24 

11.00 

0.28 

10.99 

0.34 

11 

12 

12.00 

0.21 

12.00 

0.26 

12.00 

0.31 

11.99 

0.37 

12 

13 

13.00 

0.23 

13.00 

0.28 

13.00 

0.34 

12.99 

0.40 

13 

14 

14.00 

0.24 

14.00 

0.31 

14.00 

0.37 

13.99 

0.43 

14 

15 

15.00 

0.26 

15.00 

0.33 

14.99 

0.39 

14.99 

0.46 

i5 

16 

16.00 

0.28 

16.00 

0.35 

15.99 

0.42 

15.99 

0.49 

16 

17 

17.00 

0.30 

17.00 

0.37 

16.99 

0.45 

16.99 

0.52 

17 

18 

13.00 

0.31 

IS.00 

0.39 

17.99 

0.47 

17.99 

0.55 

18 

19 

19.00 

0.33 

19.00 

0.41 

18.99 

0.50 

•18.99 

0.58 

19 

20 

20.00 

0.35 

20.00 

0.44 

19.99 

0.52 

19.99 

1 

0.61 

20 

21 

21.00 

0.37 

21.00 

0.46 

20.99 

0.55 

20.99 

0.64 

21 

22 

22.00 

0.38 

21.99 

0.48 

21.99 

0.58 

21.99 

0.67 

22 

23 

23.00 

0.40 ! 

22.99 

0.50 

22.99 

0.60 

oo an 

A* • U •/ 

0.70 

23 

24 

24.00 

0.42 

23.99 

0.52 

23.99 

0.62 

23.99 

0.73 

24 

25 

25.00 

0.44 

24.99 

0.55 

24.99 

0.65 

24.99 

0.76 

25 

26 

26.00 

0.45 

25.99 

0.57 

25.99 

0.68 

25.99 

0.79 

26 

27 

27.00 

0.47 

26.99 

0 59 j 

26.99 

0.71 

26.99 

0.83 

27 

28 

28.00 

0.49 

27.99 

0.61 

27.99 

0.73 

27.99 

0.86 

28 

29 

29.00 

0.51 

28.99 

0.63 

28.99 

0.76 

! 28.99 

0.89 

29 

30 

30.00 

0.52 

29.99 

0.65 

29.99 

0.79 

!29.99 

0.92 

30 

31 

31.00 

0.54 

30.99 

0.68 

20.99 

0.81 

I 30.99 

0.95 

31 

32 

32.00 

i ). 56 

31.99 

0.70 

31.99 

0.84 

| 31.99 

0.98 

32 

33 

32.99 

0.58 

32.99 

0.72 

32.99 

0.86 

32.9S 

1.01 

33 

34 

33.99 

0.59 

33.99 

0.74 

33.99 

0.89 

33.98 

1.04 

34 

35 

31.99 

0.61 

34.99 

0.76 

34.99 

0.92 

34.98 

1.07 

35 

36 

35.99 

0.63 

35.99 

0.79 

35.99 

0.94 

35.98 

1.10 

36 

37 

36.99 

0.65 

36.99 

0.81 

36.99 

0.97 

36.98 

1.13 

37 

39 

37.99 

0.66 

37.99 

0.83 

37.99 

0.99 

37.98 

1.16 

38 

39 

38.99 

0.68 

38.99 

0.85 

38.99 

1.02 

38.98 

1 1.19 

39 

40 

39.99 

0.70 

39.99 

0.87 

39.99 

1.05 

39.98 

i 1-22 

40 

41 

40.99 

0.72 

40.99 

0.89 

40.99 

1.07 

40.98 

1 25 

I 41 I 

42 

41.99 

0.73 

41.99 

0.92 

41.99 

1.10 

41.98 

1 28 

1 42 

43 

42.99 

0.75 

42.99 

0.94 

42.99 

1.13 

42.98 

1.31 

43 j 

44 

43.99 

0.77 

43.99 

0.96 

43.99 

1.15 

43.98 

1.84 

44 

45 

44.99 

0.79 

44.99 

0.9S 

44.99 

1.18 

44.98 

1 .37 

45 

46 

45.99 

0.80 

45.99 

1.00 

45.99 

1.20 

45.98 

1 .40 

46 

47 

46.99 

0.82 

46.99 

1.03 

46.99 

1.23 

46.98 

1.44 

47 

48 

47.99 

0.84 

47.99 

1.05 

47.98 

1 .26 

47.98 

1.47 

i 48 

49 

43.99 

0.86 

48.99 

1.07 

48.98 

1.28 

48.98 

1.50 

49 

50 

49.99 

0.87 

49.99 

1.09 

49.98 

1.31 

49.98 

1.53 

50 

Distance. 1 

i 1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 Distance. 

89 Deg. 

88f Deg. 

88^ 

Deo* 

881 Deg. 

! 



















































































































TRAVERSE TABLE. 


5 


o 

f— • 

t/3 

rf 

P 

1 Dog. 

U Deg. 

H Deg. 

U Deg. 

O 

r n 

r** 

P 

D 

O 

P 

Lat. 

Dep. 

Lat. 

Dcp. 

j 

i Lj 0.1* 

Dep. 

Lat. 

Dep. 

P 

O 

P 

51 

50.99 

0.89 

50.99 

1.11 

50.98 

1.34 

50.98 

1.56 

51 

52 

51.99 

0.91 

51.99 

1.13 

51.98 

1.36 

51.98 

1.59 

52 

53 

52 99 

0.92 

52.99 

1 . ] G 

52.98 

1.39 

52.98 

1.62 

53 

54 

53 99 

0.94 

53.99 

1.18 

53.98 

1.41 

53.97 

1 .G5 

54 

55 

54 99 

0.96 

54.99 

1.20 

54.98 

1.44 

54.97 

1.68 

55 

56 

55.99 

0.98 

55.99 

1 oo 

1 • (V (V 

55.98 

1.47 

55.97 

1.71 

56 

57 

56.99 

0.99 

56.99 

1.24 

56 98 

1.49 

56.97 

1.74 

57 

'58 

57.99 

1.01 

57.99 

1.27 

57.98 

1.52 

57.97 

1.77 

58 

59 

58.99 

1.03 

58.99 

1.29 

58.98 

1.54 

58.97 

1.80 

59 

60 

59.99 

1.05 

59.99 

1.31 

59. ys 

1.57 

59.97 

1.83 

60 

61 

60.99 

1.06 

60.99 

1.32 

60.98 

l.GD 

60.97 

1.86 

61 

62 

61.99 

1.08 

61.99 

1.35 

61.93 

1.62 

61.97 

1.89 

62 

63 

62.99 

1.10 

62.99 

1.37 

62.9S 

1.65 

62.97 

1.92 

63 

64 

63.99 

1.12 

63.98 

1.40 

63.98 

1.68 

63.97 

1.95 

64 

65 

64.99 

1.13 

64.98 

1.42 

64.98 

1.70 

64.97 

1.99 

65 

66 

65.99 

1.15 

65.98 

1.44 

65.93 

1.73 

65.97 

2.02 

06 

67 

66.99 

1.17 

66.98 

1.46 

66.98 

1.75 

66.97 

2.05 

67 

68 

67.99 

1.19 

67.98 

1.48 

67.98 

1.78 

67.97 

2.08 

68 

69 

68.99 

1.20 

68.98 

1.51 

68.98 

1.81 

68 97 

2.11 

G9 

j 70 

69.99 

1.22 

69.98 

1.53 

69.98 

1.83 

69 .97 

2.14 

70 

71 

70.99 

1.24 

70.98 

1.55 

70.98 

1.86 

70.07 

2 17 

71 

72 

71.99 

1 .26 

71.98 

1.57 

71.98 

1.88 I 

71.97 

2.20 

72 

73 

72.99 

1.27 

72.9S 

1.59 

72.97 

1.91 

72.97 

2.23 

73 

74 

73.99 

1.29 

73.98 

1.61 

73.97 

1.94 ! 

73.97 

2.20 

74 

75 

74.99 

1.31 

74.98 

1.64 

74.97 

1.96 j 

74.97 

2.29 

75 

76 

75.99 

1.33 

75.98 

1.66 

75.97 

1.99 

75.96 

2.32 

76 

77 

76.99 

1.34 

76.98 

1.08 

76.97 

2.02 

76.96 

2.35 

77 

78 

77.99 

1.36 

77.98 

1.70 

77.97 

2.04 

77.96 

2.33 

78 

79 

78.99 

1.38 

78.98 

1.72 

78.97 

2.07 

78.96 

2.41 

79 

80 

79.99 

1.40 

79.98 

1.75 

79.97 

2.09 

79.96 

2.44 

80 

81 

80.99 

1 .41 

80.98 

1.77 

80.97 

2.12 

80.96 

2.47 

81 

82 

81.99 

1.43 

81 .98 

1.79 

81.97 

2.15 

81.96a 

2.50 

82 

83 

82.99 

1.45 

82.98 

1.81 

82.97 

2.17 

82.96 

2.53 

83 

84 

83.99 

1.47 

83.98 

1.83 

83.97 

2.20 

83.96 

2.57 

84 

85 

84.99 

1.48 

84.93 

1.85 

84.97 

2.23 

84.96 

2. GO 

85 

86 

85.99 

1 .50 

85.98 

1.88 

85.97 

2.25 

85.96 

2.63 

86 

87 

86.99 

1.52 

86.98 

1.90 

86.97 

2.28 

86.96 

2.66 

87 

88 

87.99 

1.54 

87.98 

1.92 

87.97 

2.30 

87.96 

2.69 

88 

89 

88.99 

1.55 

88.98 

1.94 

88.97 

2.33 

88.96 

2.72 

89 

90 

89.99 

1.57 

89.98 

1.96 

89.97 

2.36 

89.96 

2.75 

90 

91 

90.99 

1 .59 

90.98 

1.99 

90.97 

2.38 

90.96 

' 2.78 

91 

92 

91.99 

1.61 

91.98 

2.01 

91.97 2.41 

91.96 

2.81 

92 

93 

92.99 

1.62 

92.98 

2.03 

92.97 

2.43 

| 92.96 

2.84 

93 

94 

93.99 

1.64 

93.98 

2.05 

93.97 

2.46 

93.96 

2.87 

94 

95 

94.99 

1.66 

94.98 

2.07 

94.97 

2.49 

94.96 

2.90 

95 

96 

95.99 

1.63 

95.98 

2.09 

95.97 

2.51 

95.96 

2.94 

! 96 

97 

96.99 

1.69 

96.98 

2.12 

96.97 

2.54 

96.95 

2.96 

97 

98 

97.99 

1.71 

97.98 

2.14 

97.97 

2.57 

97.95 

2.99 

98 

99 

98.98 

1.73 

98.98 

2.16 

98.97 

2.59 

98.95 

I 3.02 

I 99 

100 

99.98 

| 1.75 

99.98 

2.18 

99.97 

2.62 

99.95 

3.05 

1100 

6 

V 

c 

Dcp. 

: 

| Lat. 

Dep- 

Lat. 

Dep 

Lat. 

Dep. 

i Lat. 

6 

o 

p 

d 

CO 

« »«H 

o 

89 Deg. 

88f Deg. 

881 

i 

Deg. 

88^ Deg. 

P 

■4-J 

Q 

i 

































































































0 


TRAVERSE TABLE 


o 

in 

r** 

ps 

2 Deg. 

2\ Deg. 

Deg. 

2( Deg. 

i 

o 

ST 

<-*■ 

P 

►J 

O 

CD 

Lai. 

Dep. 

Lat. 

Dep. 

Lat. 

j Dep. 

Lat. 

Dep. 

3 

o 

a 

l 

1.00 

0.03 

1 .00 

0.04 

1.00 

0.04 

1.00 

0.05 

1 

2 

2.00 

0.07 

2.00 

0.08 

2.00 

0.09 

2.00 

0.10 

O 

3 

3.00 

0.10 

3.00 

0.12 

3.00 

0. 13 

3.00 

0.14 

o 

o 

4 

4.00 

0.14 

4.00 

0.16 

4.00 

0.17 

4.00 

0.19 

4 

5 

5.00 

0.17 

5.00 

0.20 

5.00 

0.22 

4.99 

0.24 

5 

6 

6.00 

0.21 

6.00 

0.24 

5.99 

0.26 

5.99 

0.29 

6 

7 

7.00 

0.24 

6.99 

0.27 

6.99 

0.31 

6.99 

0.34 

7 

8 

7.99 

0.28 

7.99 

0.31 

7.99 

0.35 

7.99 

0.38 

8 

9 

8.99 

0.31 

8.99 

0.35 

8.99 

0.39 

8.99 

0.43 

9 

10 

9.99 

0.35 

9.99 

0.39 

9.99 

0.44 

9.99 

0.48 

10 

11 

10.99 

0.38 

to . 99' 

0.43 

10.99 

0.48 

10.99 

0.53 

11 

12 

11.99 

042 

11.99 

0.47 

11.99 

0.52 

11.99 

0.58 

12 

13 

12.99 

0.45 

12.99 

0.51 

12.99 

0.57 

12.99 

0.62 

13 

14 

13.99 

0.49 

13.99 

0.55 

13.99 

0.61 

13.98 

0.67 

14 

15 

14.99 

0.52 

14.99 

0.59 

14.99 

0.65 

14.98 

0.72 

15 

16 

15.99 

0.56 

15.99 

0.63 

15.99 

0.70 

15.98 

0.77 

16 

17 

16.99 

0.59 

16.99 

0.67 

16.98 

0.74 

16.98 

0.82 

17 

18 

17.99 

0.63 

17.99 

0.71 

17.98 

0.79 

17.98 

0.86 

18 

19 

18.99 

0.66 

18.99 

0.75 

18.98 

0 .S3 

18.98 

0.91 

19 

20 

19.99 

0.70 

19.98 

0.79 

19.98 

0.87 

19.98 

0.96 

20 

21 

20.99 

0.73 

20.98 

0.82 

20.98 

0.92 

20.98 

1.01 

21 

22 

21.99 

0.77 

21.98 

0.86 

21.98 

0.96 

21.97 

1.06 

22 

23 

22.99 

0.80 

22.98 

0.90 

22.98 

1.00 

22.97 

1.10 

23 

24 

23.99 

0.84 

23.98 

0.94 

23.98 

1.05 

23.97 

1.15 

24 

25 

24.98 

0.87 

24.98 

0.98 

24.98 

1.09 

24.97 

1.20 

25 

2(3 

25.08 

0.91 

25.98 

1.02 

25.98 

1.13 

25.97 

1.25 

26 

27 

26.98 

0.94 

26.98 

1.06 

26.97 

1.18 

26.97 

1.30 

27 

28 

27.98 

0.98 

27.98 

1.10 

27.97 

1.22 

27.97 

1.34 

28 

29 

28.98 

1.01 

28.98 

1.14 

28.97 

1.26 

!28.97 

1.39 

29 

30 

29.98 

1.05 

29.98 

1.18 

29.97 

1 .31 

129.97 

I .44 

30 

31 

30.98 

1.08 

30.98 

1.22 

30.97 

1.35 

130.96 

1.49 

31 

32 

31.98' 

1.12 

31.98 

1.26 

31.97 

1.40 

131.96 

1 .54 

32 

33 

32.98 

1.15 

32.97 

1.30 

32.97 

1 .44 

32.96 

1.58 

33 

34 

33.98 

1.19 

33.97 

1.33 

33.97 

1.48 

33.96 

1.63 

34 

35 

34.98 

1 oo 

.1 « A* A* 

34.97 

1.37 

34.97 

1.53 

34.96 

1.68 

35 

36 

35.98 

1.26 

35.97 

1.41 

35.97 

1.57 

35.96 

1,73 

36 

37 

36.98 

1.29 

36.97 

1.45 

36.96 

1.61 

36.96 

1.78 

37 

38 

37.98 

1.33 

37.97 

1.49 

37.96 

1.66 

37.96 

1.82 

38 

39 

38.98 

1.36 

38.97 

1.53 

38.96 

1.70 

38.96 

1 .87 

39 

40 

39.98 

1.40 

39.97 

1.57 

39.96 

1.75 

39.95 

1.92 

40 

41 

40.98 

1.43 

40.97 

1.61 

40.96 

1.77 

40.95 

1 .97 

41 

42 

41.97 

1.47 

41.97 

1.65 

41.96 

1.83 

41.95 

2.02 

42 

43 

42.97 

1.50 

42.97 

1.69 

42.96 

1.88 

42.95 

2.06 

43 

44 

43.97 

1.54 

43.97 

1.73 

43.96 

1.92 

43.95 

2.11 

44 

45 

44.97 

1.57 

44.97 

1.77 

44.96 

1.96 

44.95 

2.16 

45 

46 

45.97 

1.61 

45.96 

1.81 

45.96 

2.01 

45.95 

2.21 

46 

47 

46.97 

1.64 

46.96 

1.85 

46.96 

2.05 

46.95 

2.25 

47 

48 

47.97 

1.68 

47.96 

1.88 

47.95 

2.09 

47.95 

2.30 

48 

49 

48.97 

1.71 

48.96 

1.92 

48.95 

2.14 

48.94 

2.35 

49 

50 

49.97 

1.74 

49.96 

1.96 

49.95 

2.18 

49.94 

2.40 

50 

• 

& 

o 

Dep 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

La t • 

d 

o 

Vi 

in 

• 

Q 

83 Deg. 

871 Deg. 

1 

87| 

Deg. 

871 Deg. 

ci 

73 

C 
















































































TRAVERSE TABLE 


7 


a 
m * 

r~* 

P 

2 Deg. 

Deg. 

91 

Deg. 

2| Deg. 

Distance. 


3 

o 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 


'51 

50.97 

1.78 

50.96 

2.00 

50.95 

2.22 

50.94 

2.45 

51 


52 

51.97 

1.81 

51.96 

2.04 

51.95 

2.27 

51.94 

2.50 

52 


52 

52.97 

1.85 

52.96 

2.08 

52.95 

2.31 

52.94 

2.54 

| 53 


54 

53.97 

1.88 

53.96 

f> 1 O 

/V • 1 -V 

53.95 

2.38 

53.94 

2.59 

54 


55 

54.97 

1.92 

54.96 

2.16 

54.95 

2.40 

54.94 

2.64 

55 


53 

55.97 

1.95 

55.96 

2.20 

55.95 

2.44 

55.94 

2.69 

56 


57 

j 56.97 

1.99 

50.96 

2.24 

56.95 

2.49 

56.93 

2.73 

' 57 

58 

i57.90 

2.02 

57.96 

2.28 

57.94 

2.53 

57.93 

2.78 

1 58 t 

59 

;58.96 

2.06 

58.95 

2.32 

58.94 

2.57 

58.93 

2.83 

59 


00 

59.96 

2.09 

59.95 

2.36 

59.94 

2.62 

59.93 

2.88 

60 


01 

60.96 

2. 13 

60,95 

2.39 

60.94 

2.66 

60.93 

2.93 

of 


02 

61.90 

2.16 

01.95 

2.43 

61.94 

2.70 

61.93 

2.97 

62 


03 

62.96 

2.20 

02.95 

2.47 

62.94 

2.75 

02.93 

3.02 

63 


04 

63.98 

2.23 

03.95 

2.51 

03.94 

2.79 

6.3.93 

3.07 

64 


05 

64.96 

2.27 

04.95 

2.55 

64.94 

2.84 

64.93 

3.12 

65 


GO 

65.96 

2.30 

05.95 

2.59 

65.94 

2.83 

65.92 

3.17 

60 


07 

G6.96 

2.34 

66.95 

2.03 

66.94 

2.92 

66.92 

3.21 

67 


OS 

67.90 

2.37 

87.95 

2.67 

67.94 

2.97 

67.92 

3.26 

68 


09 

68.96 

2.41 

08.95 

2.71 

68.93 

3.01 

68.92 

3.31 

69 


70 

69.98 

2.44 

09.95 

705 

2.75 

69.93 

3.05 

89.92 

3.36 

70 


71 

70.96 

2.48 

2.79 

70.93 

3.10 

70.92 

3.41 

' 71 


72 

71.96 

2.51 

71.94 

2.83 

71.93 

3.14 

71.92 

3.45 

72 


73 

72.90 

2.55 

72.94 

2.87 

72.93 

3.18 

72.92 

3.50 

73 


74 

73.95 

2.53 

73.94 

2.91 

73.93 

3.23 

73.91 

3.55 

74 


75 

74.95 

2.62 

74.94 

2.94 

74.93 

3.27 

74.91 

3.60 

75 


70 

75.95 

2.65 

75.94 

2.93 

75.93 

3.31 

75.91 

3.65 

76 


77 

76.95 

2.09 

76.94 

3.02 

76.93 

3.36 

76.91 

3.70 

77 


78 

77.95 

2.72 

77.94 

3.06 

77.93 

3.40 

77.91 

3.74 

73 


79 

73.95 

2.76 

78.94 

3.10 

78.92 

3.45 

78.91 

3.79 

79 


80 

79.95 

2.79 

79.94 

3.14 

79.92 

3.49 

79.91 

3.84 

80 


81 

80.95 

2.83 

80.94 

3.18 

80.92 

3.53 

80.91 

3.89 

81 


82 

81.95 

2.86 

81.94 

3.22 

81.92 

3.58 

81.91 

3.93 

82 


83 

82.95 

2.90 

82.94 

3.26 

82.92 

3.62 

82.90 

3.93 

83 


84 

83.95 

2.93 

83.94 

3.30 

83.92 

3.60 

83.90 

4.03 

84 


85 

84.95 

2.97 

84.93 

3.34 

84.92 

3.71 

84.90 

4.08 

85 


86 

85.95 

3.00 

85.93 

3.38 

85.92 

3.75 

85.90 

4.13 

80 


87 

80.95 

3.04 

86.93 

3.42 

86.92 

3.79 

86.90 

4. 17 

87 


88 

87.95 

3.07 

87.93 

3.45 

87.92 

3.84 

87.90 

4.22 

88 


89 

83.95 

3.11 

88.93 

3.49 

88.92 

3.88 

88.90 

4.27 

89 


90 

89.95 

3.14 

89.93 

3.53 

89.91 

3.93 

89.90 

4.32 

90 


~91 

90.95 

3.18 

90.93 

3.57 

90.91 

3.97 

90.90 

4.37 

91 


92 

91.94 

3.21 

91.93 

3.61 

91.91 

4.01 

91.89 

4.41 

92 


93 

92.94 

3.25 

92.93 

3.65 

92.91 

4.06 

92.89 

4.46 

93 


94 

93.94 

3.28 

93.93 

3.69 

93.91 

4.10 

93.89 

4.51 

94 


85 

94.94 

3.32 

94.93 

3.73 

94.91 

4.14 

94.89 

4.56 

95 


96 

95.94 

3.35 

95.93 

3.77 

95.91 

4.19 

95.89 

4.61 

96 


97 

96.94 

3.39 

96.93 

3.81 

96.91 

4.23 

96.89 

4.65 

97 


98 

97.94 

3.42 

97.92 

3.85 

97.91 

4.27 

97.89 

4.70 

98 


99 

93.94 

3.46 

98.92 

3.89 

98.91 

4.32 

93.89 

4.75 

99 


100 

99.94 

3.49 

99.92 

3.93 

99.91 

4-36 

99.88 

4.80 

100 


6 

o 

G 

Dep. 

Lac. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

d 

o 

£ 


a 

M3 

Q 

88 Deg. 

87f Deg. 

874 Deg. 

87i Deg. 

cd 

5 
























































































































8 


TRAVERSE TABLE. 


Distance. 

3 Deg. 

3| Deg. 

1 

3| Deg. 

3| Deg. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

1.00 

0.05 

1.00 

0.06 

1.00 

0.06 

1.00 

0.0G 

4> 

At 

2.00 

0.10 

2.00 

0.11 

2.00 

0.12 

2.00 

0.13 • 

A 

3.00 

0.16 

3.00 

0.17 

2.99 

! 0.18 

2.99 

0.20 

4 

3.99 

0.21 

3.99 

0.23 

3.99 

i 0.24 

3.99 

0.26 

5 

4.99 

0.26 

4.99 

0.28 

4.99 

0.31 

4.99 

0.33 

6 

5.99 

0.31 

5.99 

0.34 

5.99 

0.37 

5.99 

0.39 

7 

6.99 

0.37 

6.99 

0.40 

6.99 

0.43 

6.99 

0.46 

8 

7.99 

0.42 

7.99 

0.45 

7.99 

0.49 

7.98 

0.52 

9 

8.99 

0.47 

8.99 

0.51 

8.98 

0.55 

8.98 

0.59 

10 

9.99 

0.52 

9.98 

0.57 

9.98 

0.61 

9.98 

0.65 

11 

10.98 

0.58 

10.98 

0.62 

10.98 

0.67 

10.98 

0.72 

12 

11.98 

0.63 

11.98 

0 . 68 

11.98 

0.73 

11.97 

0.78 

13 

12.98 

0.68 

12.98 

0.73 

12.98 

0.79 

12.97 

0.85 

14 

13.98 

0.73 

13.98 

0.79 

13.97 

0.85 

13.97 

0.92 

15 

14.98 

0.79 

14.98 

0.85 

14.97 

0.92 

14.97 

0.98 

10 

15.99 

0.84 

15.97 

0.91 

15.97 

0.98 

15.97 

1.05 

17 

16.98 

0.89 

16.97 

0.96 

I 16.97 

1.04 

16.96 

1.11 

18 

17.98 

0.94 

17.97 

1.02 

j 17.97 

1.10 

17.96 

1.18 

19 

18.98 

0.99 

18.97 

1.08 

18.98 

1.16 

18.90 

1.24 

20 

19.97 

1.05 

19.97 

1.13 

!19.96 

1.22 

19.96 

1.31 1 

21 

20.97 

1.10 

20.97 

1.19 

20.96 

r.28" 

20.96 

1.371 

22 

21.97 

1.15 1 

21.96 

1.25 

121.96 

1.34 

21.95 

1.44 

23 

22.97 

1.20 

22.96 

1.30 

j 22.98 

1.40 

22.95 

1.50 ] 

24 

23.97 

1.26 

23.96 

1.36 

23.96 

1.47 

23.95 

1.57 

25 

24.97 

1.31 

24.98 

1.42 

|24.95 

1.53 

24.95 

1.04 

26 

25.96 

1.36 

25.96 

1.47 

25.95 

1.59 

25.94 

1.70 

27 

26.96 

1.41 

26.96 

1.53 

26.95 

1.65 

26.94 

1.77 

23 

27.96 

1.47 

27.95 

1.59 

27.95 

1.71 1 

27.94 

1.83 ! 

29 

28.96 

1.52 

28.95 

1.64 

28.95 

1.77! 

28.94 

1.90 

30 

29.96 

1.57 

29.95 

1.70 

29.94 

1.83 j 

29.94 

1.96 

31 

30.96 

1.62 

30.95 

1.76 

30.94 

1.89 

30.03 

2.03 

32 

31.96 

1.67 

31.95 

1.81 

31.94 

1.95 

31.93 

2.09 

33 

32.95 

1.73 

32.95 

1.87 

32.94 

2.01 

32.93 

2. 16 

34 

33.95 

1.78 

33.95 

1.93 

33.94 

2.08 

33.93 

2.22 

35 

34.95 

1.83 

34.94 

1.98 

34.93 

2.14 

34.92 

f> 9Q 

36 

35.95 

1.88 

35.94 

2.04 

35.93 

2.20 

35.92 

2.35 

37 

36.95 

1.94 

36.94 

2.10 

36.93 

2.26 

36.92 

2.42 

38 

37.95 

1.99 

37.94 

2.15 

37.93 

2.32 

37.92 

2.49 

39 

38.95 

2.04 

38.94 

2.21 

38.93 

2.38 j 

38.92 

3.55 

40 

39.95 

2.09 

39.94 

2.27 

39.93 

2.44*1 

39.91 

2.62 

41 

40.94 

2.15 

40.93 

2.32 

40.92 

2.50 | 

40.91 

2.68 | 

42 

41.94 

2.20 

41.93 

2.38 

41.92 

2.56 

41.91 

2.75 

43 

42.94 

2.25 

42.93 

2.44 

42.92 

2.63 

42.91 

2.81 

44 

43.94 

2.30 

43.93 

2.49 

43.92 

2.69 

43.91 

2.88 

45 

44.94 

2.36 

44.93 

2.55 

44.92 

2.75 

44.90 

2.94 

46 

45.94 

2.41 

45.93 

2.61 

45.91 

2.81 

45.90 

3.01 

47 

46.94 

2.46 

46.92 

2.66 

46.91 

2.87 

46.90 

3.07 

48 

47.93 

2.51 

47.92 

•2.72 

47.91 

2.93 

47.90 

3.14 

49 

48.93 

2.56 

48.92 

2.78 

48.91 

2.99 

48.90 

3.20 

50 

49.93 

2.62 

49.92 

2.83 

49.91 

3.05 

49.89 

3.27 

6 

0 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

a 

v~> 

2 

3 

87 Deg. 

86 3 Deg. 

86 A- Deg. | 

8G^ Deg. 

1 

1 1 


1 11 »• I n rlAn. ^k— ►*-* *—* ►*— ; *— v*» >-«»»' v.^ v^v s» wv w rv t'-' iv tv tn^ iv tx.' i p— i— >-— >—- ►—- —— i—■ 

ivu>uluci>| otc oo o tn i^w to >— I ©cc oc <i o m if*co to — | cso oo -4 cs oi f* w to >— 1 o«o oo<i 35 c* *p» go to *— | o<x>00 -vi 35in >f* co to ►-'r 00 UTJ J s IG 






































































































TRAVERSE TABLE 


9 


3 

I • 

cr. 

P 

3 Deg. 

i 

i 

3} Deg. 

Deg. 


23 Deg 


C 

oo* 

r*- 

po 

o 

Cl 

1 Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

a 

• 

f)l 

50.93 

2.07 

50 

.92 

2. 

89 

50. £0 

3-11 

50 

.89 

3 

.34 

51 

52 

51.93 

o 7‘> 

iV • ( 

51 

.92 

O 

_ 

95 

51.90 

3.17 

51 

.89 

3 

.40 

52 

53 

52.93 

2.77 

hii 

.91 

3. 

00 

i52.90 

3.24 

52 

.89 

3 

.47 

53 

54 

53.93 

2.83 

53 

.91 

3. 

06 

53.90 

3.30 

53 

.88 

3 

. 53 

54 

5ft 

54.92 

2.88 

54 

.91 

3. 

12 

154.90 

3.36 

54 

.88 

3 

.60 

55 

66 

55.92 

2.93 

55 

.91 

3. 

17 

I 55.90 

3.42 

55 

.88 

3 

.66 

56 

57 

56.92 

2.98 

56 

.91 

3. 

23 

|56.89 

3.48 

56 

.88 

3 

73 

57 

58 

57.92 

3.04 

57 

.91 

3. 

29 

157.89 

3.54 

57 

.88 

3 

.79 

68 

59 

58.92 

3.09 

58 

.91 

3. 

34 

| 58.89 

3.60 

58 

.87 

3 

.86 

59 

BO 

59.92 

3.14 

59 

.90 

3. 

40 

|59.89 

3.66 

59 

.87 

3 

.92 

60 

61 

60.92 

3.19 

60 

.90 

3. 

46 

i60.89 

3.72 

60 

.87 

3 

.99 

61 

62 

;61.92 

3.24 

61 

.90 

3. 

51 

161.88 

3.79 

61 

.87 

4 

.05 

62 

63 

62.91 

3.30 

62 

.90 

3. 

57 

!62.88 

3.85 | 

62 

.87 

4 

. 12 

63 

(54 

i63.91 

3.35 

63 

.90 

3. 

03 

63.88 

3.91 

63 

.86 

4 

.19 

64 

65 

I 64.91 

3.40 

64 

.90 

3. 

69 

64.88 

3.97 

64 

.86 

4 

.25 

65 

60 

! 65.91 

3.45 

65 

.89 

3. 

74 

65.88 

4.03 

65 

.86 

4 

.32 

66 

67 

1 66.91 

3.51 

66 

.89 

3. 

80 

6G.88 

4-09 1 

66 

.86 

4 

.38 

67 

68 

;67.9i 

3.56 

67 

.89 

3. 

86 

07.87 

4.15 

67 

.85 

4 

.45 

68 

69 

68.91 

3.61 

68 

.89 

3. 

91 

68.87 

4.21 

68 

.85 

4 

.51 

69 

70 

69.90 

3.66 

69 

.89 

3. 

97 

69.87 

4-27 

69 

.85 

4 

.58 

70 

71 

70.90 

3.72 

70 

.89 

4. 

03 

70.87 

4.33 

70 

.85 

4 

.64 

71 

72 

71.90 

3.77 

71 

.88 

4. 

OS 

71.87 

4.40 

71 

.85 

4 

.71 

72 

73 

72.90 

3.82 

72 

.88 

4. 

14 

72.86 

4.46 

72 

.84 

4 

.77 

73 

74 

73.90 

3.87 

73 

.88 

4. 

20 

73.86 

4.52 

73 

.84 

4 

.84 

74 

75 

74.90 

3.93 

74 

.88 

4. 

25 

74.80 

4.58 

74 

.84 

4 

.91 

75 

76 

75.90 

3.98 

75 

.88 

4. 

31 

75-86 

4.64 

i 75 

.84 

4 

.97 

76 

77 

76.89 

4.03 

76 

.88 

4. 

37 

76.86 

4.70 

76 

.84 

5 

.04 

77 

78 

77.89 

4.08 

77 

.87 

4. 

42 

77.85 

4.76 

77 

.83 

5 

.10 

78 

79 

78.89 

4.13 

78 

.87 

4. 

48 

78.85 

4.82 

78 

.83 

5 

.17 

79 

80 

79.89 

4.19 

79 

.87 

4. 

54 

79.85 

4.88 

79 

.83 

5 

.23 

80 

81 

80.89 

4.24 

80 

.87 

4. 

59 

80.85 

4.94 

80 

.83 

5 

.30 

81 

82 

81.89 

4.29 

81 

.87 

4. 

65 

81.85 

5.01 

81 

.82 

5 

.36 

82 

83 

82.89 

4.34 

82 

.87 

4. 

71 

82.85 

5.07 

I 82 

.82 

5 

.43 

83 

84 

83.88 

4.40 

83 

.86 

4- 

76 

83.84 

5.13 

| 83 

.82 

5 

.49 

84 

85 

84.88 

4.45 

84 

.86 

4. 

82 

84.84 

5.19 

i 84 

.82 

5 

.56 

85 

86 

85.88 

4.50 

85 

.86 

4- 

88 

85.84 

5.25 

i 85 

.82 

5 

.62 

86 

87 

86.88 

4.55 

86 

.86 

4. 

93 

86.84 

5.31 

86 

.81 

5 

.69 

87 

88 

87.88 

4.61 

87 

.86 

4. 

99 

87.84 

5.37 

87 

.81 

5 

.76 

88 

89 

88.88 

4.66 

88 

.86 

5. 

05 

8S.83 

5.43 

88 

.81 

5 

.82 

89 

90 

89.88 

4.71 

H9 

.86 

5. 

10 

89.83 

5.49 

89 

.81 

5 

.89 

90 

91 

90.88 

4.76 

90 

.85 

5. 

16 

90.83 

5.56 

90 

.81 

5 

.95 

91 

92 

91.87 

4.81 

91 

.85 

5. 

22 

91.83 

5.62 

91 

.80 

6 

.02 

92 

93 

92.87 

4.87 

92 

.85 

5. 

27 

92.83 

5.68 

92 

.80 

6 

.08 

93 

94 

93.87 

4.92 

93 

.85 

5. 

33 

93.82 

5.74 

93 

.80 

6 

.15 

94 

95 

94.87 

4.97 

94 

.85 

5. 

39 

94.82 

5.80 

94 

.80 

6 

.21 

95 

96 

95.87 

5.02 

95 

.85 

5. 

44 

95.82 

5.86 

95 

.79 

6 

.28 

96 

97 

96.87 

5.08 

96 

.84 

5 

50 

96.82 

5.92 

96 

.79 

6 

.34 

97 

98 

97.87 

5.13 

97 

.84 

5. 

56 

97.82 

5.98 

97 

.79 

6 

.41 

98 

99 

98.86 

5.18 

98 

.84 

5. 

61 

98.82 

6.04 

98 

. 79 

6 

.47 

99 

100 

99.86 

5.23 

99 

.84 

5. 

67 

99.81 

6.10 

99 

.79 

G 

.54 

100 

© 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.. 

© 

o 

G 

a 

87 Deg. 

8GJ Deg. 

8G| Deg 

8Deg. 

Lists 






























































































10 


TRAVERSE TAELE. 


Distance. 

4 Deg. 

4$ Deg. 

4-£ Deg. 

4| Deg. 

Distance. 

Lat. 

Dcp< 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dcp. 

1 i 

1.00 

0.07 

1.00 

0.07 

1.00 

0.08 

1.00 

0.08 

1 

2 

2.00 

0.14 

1 .99 

0.15 

1.99 

0.16 

1.99 j 

0.17 

2 

3 i 

2.99 i 

0.21 1 

2.99 

0.22 

2.99 

0.24 

2.99 ! 

0.25 

3 

4 

3.99 1 

0.28 | 

3.99 

0.30 

3.99 

0.31 

3.98 

0.33 

4 

5 

4.99 

0.35 

4.99 

0.37 

4.98 

0.39 

4.98 

0.41 

5 

G 

5.99 

0.42 

5.98 

0.44 

5.98 

0.47 

5.98 

0.50 

6 

? 

6.98 

0.49 

6.98 

0.52 

6.98 

0.55 

6.97 

0.58 

7 

8 f 

7.98 

0.56 

7.98 

0.59 

7.98 

0.63 

7.97 

0.66 

8 

9 

8.98 

0.G3 

8.98 

0.67 

8.97 

0.71 

8.97 

0.75 

9 . 

10 

9.98 

0.70 

9.97 

0.74 

9.97 

0.78 

9,97 

0.83 

10 

11 

10.97 

0.77 

10.97 

0.82 

10.97 

0.86 

10.96 

0.91 

11 

12 

11.97 

0.84 

11.97 

0.89 

11.96 

0.94 

11.96 

0.09 

12 

13 

12.97 

0.91 

12.96 

0.90 

12.96 

1.02 

12.96 

1.08 

13 

14 

13.97 

0.98 

13.96 

1.04 

13.96 

1.10 

J 3.95 

1.16 

14 

15 

14.96 

1.05 

14.96 

1.11 

14.95 

1 . f 8 

14.95 

1.24 

15 

16 

15.96 

1.12 

15.96 

1.19 

15.95 

1.26 

15.95 

1 . 32 

16 

17 

16.96 

1.19 

16.95 

1.26 

16.95 

1.33 

16.94 

1.41 

17 

18 

17.96 

1.26 

17.95 

1.33 

17.94 

1 .41 

17.94 

1.49 

18 

19 

18.95 

1.33 

18.95 

1.40 

18.94 

1.49 

18.93 

1.57 

19 

20 

19.95 

1.40 

19.95 

1.48 

19.94 

1.57 

19.93 

1 . 60 

20 

21 

20.95 

1.46 

20.94 

1.56 

20.94 

1.65 

20.93 

1.74 

21 

22 

21.95 

1.53 

21.94 

1.63 

21.93 

1.73 

21.92 

1 .82 

22 

23 

22.94 

1.60 

22.94 

1.70 

22.93 

1.80 

22.92 

1.90 

23 

24 

23.94 

1.67 1 

23.93 

1.78 

23.93 

1.88 

23.92 

1 .99 

24 

25 

24.94 

1.74 

24.93 

1.85 

24.92 

1.96 

24.91 

2.07 

25 

26 

25.94 

1.81 

25.93 

1 .93 

25.92 

2.04 

25.91 

2.15 

26 

2 ? 

26.93 

1.88 

26.93 

2.00 

26.92 

2.12 

26.91 

2.24 

27 

28 

27.93 

1.95 

27.92 

2.08 

27.91 

2.20 

27.90 

2.32 

28 

29 

28.93 

2.02 

28.92 

2.15 

28.91 

2.28 

28.90 

2.40 

29 

30 

29.93 

2.09 

29.92 

2.22 

29.91 

2.35 

29.90 

2.48 

30 

31 

30.92 

2.16 

30.91 

2.30- 

30.90 

2.43 

30.89 

2.57 

31 

32 

31.92 

2.23 

31.91 

2.37 

31.90 

2 . 5 l 

31.89 

2.65 

32 

33 

32.92 

2.30 

32.91 

2.45 

| 32.90 

2.59 

32.89 

2.73 

33 

34 

33.92 

2.37 

33.91 

2.52 

33.90 

2.67 

33.88 

2.82 

34 

35 

34.91 

2.44 

1 34.90 

2.59 

34.89 

2.75 

34.88 

2.90 

35 

.36 

35.91 

1 2.51 

35.90 

2.07 

35.89 

2.82 

35.88 

2.9S 

36 

37 

36.91 

1 2.58 

36.90 

2.74 

36.89 

2.90 

36.87 

3.06 

37 

3S 

37.91 

2.65 

37.90 

2.82 

37.88 

2.98 

37.87 

3.15 

38 

39 

38.90 

2.72 

38.89 

2.89 

38.88 

3.06 

38.87 

3.23 

39 

40 

39.90 

2.79 

39.89 

2.96 

39.88 

3.14 

39.86 

3.31 

40 

41 

40.90 

2.86 

40.89 

3.04 

40.87 

3.22 

40.86 

3.40 

41 

42 

141.90 

2.93 

41.88 

3.11 

41.87 

3.30 

41.86 

3.48 

42 

43 

42.90 

3.00 

42.88 

3.19 

42.87 

3.37 

42.85 

3.56 

43 

44 

43.89 

3.07 

43.88 

3.26 

43.86 

3.45 

43.85 

3.64 

44 

45 

44.89 

3.14 

44.88 

3.33 

44.86 

3.53 

44.85 

3.73 

45 

46 

45.89 

3.21 

45.87 

3.41 

45. °e 

3.61 

45.84 

3.81 

46 

47 

46.89 

3.28 

46.87 

3.48 

46.86 

3.69 

46.84 

3.89 

47 

! 48 

47.88 

3.35 

47.87 

3.56 

47.85 

3.77 

47.84 

i 3.97 

48 

\ 49 

48.S8 

3.42 

48.87 

3.63 

48.85 

3.84 

48.83 

4.06 

49 

\ 50 

49.88 

3.49 

49.86 

3.71 

49.85 

3.92 

49.83 

1 4.14 

50 

i | 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

Dcp. 

j Lat. 

O 

o 

c 

ri 

'Si 

c 

!| 

86 Deg. 

85J Deg. 

851 Deg. 

85$ Deg. 























































































































TRAVERSE TABLE 


11 


o 

in 

rf- 

P 

4 Dog. 

44 Deg. 

Deg. 

4| Deg. 

Distance. 

3 

O 

0 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.88 

3.56 

50.86 

3.78 

50.84 

4.00 

50.82 

4.22 

51 

52 

51.87 

3.63 

51.86 

3.85 

51.84 

4.08 

51.82 

4.31 

52 

53 

52.87 

3.70 

52.85 

3.93 

52.84 

4.16 

52.82 

4.39 

53 

54 

53.87 

3.77 

53.85 

4.00 

53.83 

4.24 

53.81 

4.47 

54 

•d;> 

54.87 

3.84 

54.85 

4.08 

54.83 

4.32 

54.81 

4 55 

55 

56 

55.86 

3.91 

55.85 

4.15 

55.83 

4.39 

55.81 

4.64 

56 

57 

56.86 

3.98 

56.84 

4.22 

56.82 

4.47 

56.80 

4.72 

57 

53 

57.86 

4.05 

57.84 

4.30 

57.82 

4.55 

57.80 

4.80 

58 

59 

58.86 

4.12 

58.84 

4.37 

58.82 

4.63 

58.80 

4.89 

59 

60 

59.85 

4.19 

59.84 

4.45 

59.82 

4.71 

59.79 

4.97 

60 

61 

60.85 

4.26 

60.83 

4 . 52 

60.81 

4.79 

60.79 

5.05 

61 

62 

61.85 

4.32 

61.83 

4.59 

61.81 

4.86 

61.79 

5.13 

62 

63 

62.85 

4.39 

62.83 

4.67 

62.81 

4.94 

62.78 

5.22 

63 

64 

63.84 

4.46 

63.82 

4.74 

63.80 

5.02 

63.78 

5.30 

64 

65 

64.84 

4.53 

64.82 

4.82 

64.80 

5.10 

64.78 

5.38 

65 

66 

65.84 

4.60 

65.82 

4.89 

65.80 

5.18 

65.77 

5.47 

66 

67 

66.84 

4.67 

66.82 

4.97 

66.79 

5.26 

66.77 

5 . 55 

67 

63 

67.83 

4.74 

67.81 

5.04 

67.79 

5.34 

67.77 

5.63 

68 

69 

68.83 

4.81 

68.81 

5.11 

68.79 

5.41 

68.76 

5.71 

69 

70 

69.83 

4.88 

69.81 

5.19 

69.78 

5.49 

69.76 

5.80 

70 

71 

70.83 

4.95 

70.SO 

5.26 

70.78 

5.57 

70.76 

5.88 

71 

72 

71.82 

5.02 

71.80 

5.34 

71.78 

5.65 

71.75 

5.96 

72 

73 

72.82 

5.09 

72.80 

5.41 

72.77 

5.73 

72.75 

6.04 

73 

74 

73.82 

5.16 

, 73.80 

5.48 

73.77 

5.81 

73.75 

6.13 

74 

75 

74.82 

5.23 

1 74.79 

5.56 

74.77 

5.88 

74.74 

6.21 

75 

76 

75.81 

5.30 

75.79 

5.63 

75.77 

5.96 

75.74 

6.29 

76 

77 

76.81 

5.37- 

76.79 

5.71 

76.76 

6.04 

76 . 74 

6.33 

77 

78 

77.81 

5.44 

77.79 

5 . 78 

77 . 76 

6.12 

77.73 

6.46 

78 

79 

78.81 

5.51 

78.78 

5 . 85 

78 . 76 

6.20 

78 . 73 

6.54 

79 

80 

79.81 

5.58 

79.78 

5 . 93 

79 . 75 

6.28 

79.73 

6 . 62 

SO 

81 

80.80 

5.65 

80.78 

6 . 00 

80.75 

6.36 

80.72 

6.71 

nil 

82 

81.80 

5.72 

81.78 

6.08 

81.75 

6.43 

81.72 

6.79 

82 

83 

82.80 

5.79 

82.77 

6.15 

S2.74 

6.51 

82.71 

6.87 

83 

84 

83.80 

5.86 

83.77 

6.23 

83.74 

6.59 

83.71 

6.96 

84 

85 

84.79 

5.93 

, 84.77 

6 . 30 

84.74 

6.67 

84.71 

7.04 

85 

86 

S5.79 

6.00 

85.76 

6.3? 

85.73 

6.75 

85 . 70 

7.12 

86 

87 

86.79 

6.07 

!86.76 

6 . 45 

86.73 

6.83 

96.70 

7.20 

87 

88 

87.79 

6.14 

I 87.76 

6.52 

87.73 

6.90 

87.70 

7.29 

88 

89 

88 . 78 

6.21 

: 83.76 

6.60 

88 . 73 

6.98 

88.70 

7.37 

89 

90 

89.78 

6.28 

j 89.75 

6.67 

89.72 

7.06 

89.69 

7.45 

90 

91 

90.78 

6.35 I 

90.75 

6.74 

90.72 

7.14 

90.69 

7.54 

91 

92 

91.78 

6.42 91.75 

6.82 j 

91.72 

7.22 

91.68 

7 . 62 

92 

93 

92 . 77 

6.49 

92 . 74 

6.89 

92.71 

7.30 

92.68 

7.70 

93 

94 

93.77 

6.56 

93.74 

6.97 

93.71 

7.38 

93.68 

7.78 

94 

95 

94.77 

6 . 63 

94.74 

7.04 1 

94.71 

7.45 

94.67 

7.87 

95 

96 

95.77 

6.70 

95.74 

7.11 | 

95.70 

7.53 

95.67 

7.95 

96 

97 

96.76 

6 . 77 

96.73 

7.19 

96.70 

7.61 

96.67 

8.03 

97 

98 

97.76 I 

6.84 

97.73 

7.26 

97.70 

7.69 

97.66 

8.12 

98 

99 

93.76 

6.91 

6.98 

99.73 

7.34 ! 

93 . 69 

7 . 77 

98.66 

8.20 

99 

100 

99.76 ! 

99.73 

7.41 

99.69 

7.85 

99.66 

8.28 

100 

6 

Dep. j 

Lat. ! 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

O 

CJ 

ri 

in 

5 

1 

I 

86 Deg. 

1 

85 f Dep-. 

85* Deg. 

85} Deg. 

ctf 

m 

G 


J 




















































































12 


traverse taele 


— 

Distance. 

5 Deg. 

5} Deg. 

Deg. 

5f Deg. 

>—«* 

ST 

r* 

P 

Lat. 

Deo. 

4 

Lat. 

Dep. 

Lat. | 

Dep. 

Lat. 

Dep. 

P 

o 

p 

~ 1 

1.00 

0.09 

1.00 

0.09 

1.00 

0.10 

0.99 

0.10 

1 

O 

1.99 I 

0.17 

1.99 

0.18 

1.99 

0.19 

1.99 

0.20 

o j 

3 

2.99 ! 

0.26 

2.99 

0.27 

2.99 

0.29 

2.98 

0.30 

3 | 

4 

3.98 I 

0 .35 

3.98 

0.37 

3.98 

0.38 

3.98 

0.40 • 

4 | 

6 

4.98 

0.44 

4.98 

0.46 

4.98 

0.48 

4.97 

0.50 j 

r >! 

G 

5.98 

0.52 

5.97 

0.55 

5.97 

0.58 

5.97 

0.60 j 


? 

6.97 

0.61 

6.97 

0.64 

6.97 

0.67 

6.96 

0.70 | 

1 i 

8 

7.97 

0.70 

7.97 

0.73 

7.96 

0.76 

7.96 

0.80 j 

g 

9 

8.97 

0.78 

8.96 

0.82 

8 96 

0.86 

8.95 

0.90 


10 

9.96 

0.87 

9.96 

0.92 

9.95 

0.96 

9.95 

1.00 

10 ; 

11 

10.96 

0.96 

10.95 

1.01 

10.95 

1.05 

10.94 

1.10 

li; 

12 

1L. 95 

1.05 

11.96 

1.10 

11.94 

1.15 

11.94 

1.20 

12 ' 

13 

12.95 

1. 13 

12.95 

1.19 

12.94 

1.25 

12.93 

1.30 

13 

14 

13.95 

1.22 

13.94 

1.28 

13.94 

1.34 

13.93 

1.40 

14, 

15 

14.94 

1.31 

14.94 

1.37 

14.93 

1.44 

14.92 

1.50 

15 | 

16 

15.94 

1.39 1 

15.93 

1.46 

15.93 

1.53 

15.92 

1.60 

16 

17 

16.94 

1.48 1 

16.93 

1.56 

16.92 

1.63 

16.91 

1.70 

17 

IS 

17.93 

1.57 

17.92 

1.65 

17.92 

1.73 

17.91 

1.80 

18 

19 

18.93 

1.66 | 

18.92 

1.74 

18.91 

1.82 

18.90 

1.90 

19 

20 

19.92 

1.74; 

19.92 

1.83 

19.91 

1.92 

19.90 

2.00 

20 

21 

20.92 

1.83 

20.91 

1.92 

20.90 

2.01 

20.89 

2.10 

21 

22 

21.92 

1.92 

21.91 

2.01 

21.90 

2.11 

21.89 

2.20 

22 

23 

22.91 

2.00 

22.90 

2.10 

22.89 

2.20 

22.88 

2.30 

23 

24 

23.31 

2.09 

,23.90 

2.20 

23.89 

2.30 

23.88 

2.40 

24 

25 

24.90 

2.18 

!24.90 

2.29 

24.88 

2.40 

24.87 

2.50 

25 

26 

25.90 

2.27 

25.89 

2.38 

25.88 

2.49 1 

25.87 

2.60 

26 

27 

26.90 

2.35 

26.89 

2.47 

26.88 

2.59 

26.86 

2.71 

27 

28 

27.89 

2.44 

27.88 

2.56 

27.87 

2.68 

27.86 

2.81 

28 

29 

28.89 

2.53 

28.88 

2.65 

28.87 

2.78 

28.85 

2.91 

29 

30 

29.89 

2.61 

29.87 

2.75 

29.86 

2.88 

29.85 

3.01 

30 

31 

30.88 

2.70 

30.87 

2.84 

30.86 

2.97 

30.84 

3.11 

31 

32 

31.88 

2.79 

31.87 

2.93 

31.85 

3.07 

31.84 

3.21 

32 

33 

32.87 

2.88 

32.86 

3.02 

32.85 

3.16 

32.83 

3.31 

33 

34 

33.87 

* 2.96 

33.86 

3.11 

33.84 

3.26 

33.83 

3.41 

34 

35 

34.87 

3.05 

34.85 

3.20 

34.84 

3.35 

34.82 

3.51 

35 

36 

35.86 

3.14 

35.85 

3.29 

35.83 

3.45 

35.82 

3.61 

36 

37 

36.86 

3.22 

36.84 

3.39 

36.83 

3.55 

36.81 

3.71 

37 

38 

37.86 

3.31 

37.84 

3.48 

37.83 

3.64 

37.81 

3.81 

38 

39 

38.85 

3.40 

38.84 

3.57 

38.82 

3.74 

38.80 

3.91 

39 

40 

39.85 

3.49 

39.83 

3.66 

39.82 

3.83 

39.80 

4.01 

40 

41 

40.84 

3.57 

40.83 

3.75 

40.81 

3.93 

40.79 

4.11 

41 

42 

41.84 

3.66 

41.82 

3.84 

41.81 

4.03 

41.79 

4.21 

42 

43 

42.84 

3.75 

42.82 

3.93 

42.80 

4.12 

42.78 

4.31 

43 

44 

43.83 

3.83 

43.82 

4.03 

43.80 

4.22 

43.78 

4.41 

44 

45 

44.83 

3.92 

44.81 

4.12 

44.79 

4.31 

44.77 

4.51 

45 

46 

45.82 

4.01 

45.81 

4.21 

45.79 

4.41 

45.77 

4.61 

46 

47 

46.82 

4.10 

46.80 

4.30 

46.78 

4.50 

46.70 

4.71 

47 

48 

47.82 

4.18 

47.80 

4.39 

47.78 

4.60 

47.76 

4.81 

43 

49 

48.81 

4.27 

48,79 

4.48 

48.77 

4.70 

48.75 

4.91 

49 

50 

49.81 

| 4.36 

49.79 

4.58 

49.77 

4.79 

49.75 

5.01 

50 

CD* 

V 

P 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

Dep. 

Lat. 

6 

o 

e 

ci 

K 

85 Deg. 

1 

j 84? Deg. 

!! 

84A 

- 

Deg. 

34} Deg. 

1 

; * 

! 3 


I 





























































































































TRAVERSE TABLE. 


13 


3 

N- • 
00 

P 

5 Deg. 

5^ Deg. 

6 i 

Deg. 

• r 4 

Deg 

c-+ 

P 

o 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 o 

1 CD 

51 

50.81 

4 

.44 

50.79 

4.67 

50.77 

4.89 

50774 

511 

51 

52 

51.80 

4 

.53 

51.78 

4.76 

51.76 

4.98 

51.74 

5.21 

52 

53 

52.80 

4 

.62 

52.78 

4.85 

52.76 

5.08 

52.73 

5.31 

53 

54 

53.79 

4 

.71 

53.77 

4.94 

53.75 

5.18 

53.73 

5.41 

I 54 

55 

54.79 

4 

.79 

54.77 

5.03 

54.75 

5.27 

54.72 

5.51 

55 

56 

55.79 

4 

.88 

55.77 

5.12 

55.74 

5.37 

55.72 

5.61 

! 56 

| 57 

56.78 

4 

.97 

56.76 

5.22 

56.74 

5.46 

56.71 

5.71 

1 57 

58 

57.78 

5 

.06 

57.76 

5.31 

57.73 

5.56 

57.71 

5.81 

58 

59 

58.78 

5 

.14 

58.75 

5.40 

58.73 

5.65 

58.70 

5.91 

59 

60 

59.77 

5 

.23 

59.75 

5.49 

59.72 

5.75 

59.70 

6.01 

S GO 

61 

60.77 

5 

.32 

60.74 

5.58 

60.72 

5.85 

60.69 

6.11 

i ci 

1 62 

61.76 

5 

.40 

61.74 

5.67 

61.71 

5.94 

61.69 

6.21 

62 

3 63 

62.76 

5 

.49 

62.74 

5.76 

62.71 

6.04 

62.68 

6.31 

63 

I 64 

63.76 

5 

.58 

63.73 

5.86 

63.71 

6.13 

63.68 

6.41 

64 

3 65 

64.75 

5 

.67 

64.73 

5.95 

64.70 

6.23 

64.67 

6.51 

65 

3 66 

65.75 

5 

.75 

65.72 

6.04 

65.70 

6.33 

65.67 

6.61 

66 

67 

66.75 

5 

.84 

66.72 

6.13 

66.69 

6.42 

66.66 

6.71 

67 

68 

67.74 

5 

.93 

67.71 

6.22 

67.69 

6.52 

67.66 

6.81 

68 

69 

68.74 

6 

.01 

68.71 

6.31 

68.68 

6.61 

68.65 

6.91 

69 

70 

69.73 

6 

.10 

69.71 

6.41 

69.68 

6.71 

69.65 

7.01 

70 

71 

70.73 

6 

.19 

70.70 

6.50 

70.67 

6.81 

70.64 

7.11 

71 

72 

71.73 

6 

.28 

71.70 

6.59 

71.67 

6.90 

71.64 

7.21 

72 

73 

72.72 

6 

.36 

72.69 

6.68 

72.66 

7.00 

72.63 

7.31 

73 

74 

73.72 

6 

.45 

73.69 

6.77, 

73.66 

7.09 

73.63 

7.41 

74 

75 

74.71 

6 

.54 

74.69 

6.86 

74.65 

7.19 

74.62 

7.51 

75 

76 

75.71 

6 

.62 

75.68 

G.95 

75.65 

7.28 

75.62 

7.61 

76 

77 

76.71 

6 

.71 

76.68 

7.05 

76.65 

7.38 

76.61 

7.71 

77 

78 

77.70 

6 

.80 

77.67 

7.14 

77.64 

7.48 

77.61 

7.81 

78 

79 

78.70 

6 

.89 

78.67 

7.23 

78.64 

7.57 

78.60 

7.91 

79 

80 

79.70 

6 

.97 

79.66 

7.32 

79.63 

7.67 

79.60 

8.02 

80 

81 

80.69 

7 

.06 

80.66 

7.41 

80.63 

7.76 

80.59 

8.12 

81 

82 

81.69 

7 

.15 

81.66 

7.50 

81.62 

7.86 

81.59 

8.22 

82 

83 

82.68 

7 

.23 

82.65 

7.59 

82.62 

7.96 

82.58 

8.32 

83 

84 

83.68 

7 

.32 

83.65 

7.69 

83.61 

8.05 

83.58 

8.42 

84 

85 

84.68 

7 

41 

84.64 

7 .'78 

84.61 

8.15 

84.57 

8.52 

85 

86 

85.67 

7 

50 

85.64 

7.87 

85.60 

8.24 

85.57 

8.62 

86 

87 

86.67 

7 

5S 

86.64 

7.96 

86.60 

8.34 

86.56 

8.72 

87 

88 

87.67 

7. 

67 

87.63 

'8.05 

87.59 

8.43 

87.56 

8.82 

88 

89 

83.66 

7 

76 

88.63 

8.14 

88.59 

8.53 

88.55 

8.92 

89 

90 

89.66 

7. 

84 

89.62 

8.24 

89.59 

8.63 

89.55 

9.02 

90 

91 

90.65 

7. 

93 

90.62 

8.33 

90.58 

8.72 

90.54 

9.12 

9] i 

92 

91.65 

8. 

02 

91.61 

8.42 

91.58 

8.82 

91.54 

9.22 

92 

( 93 

92.65 

8. 

11 

92.61 

8.51 

92.57 

8.91 

92.53 

9.32 

93 

94 

93.64 

8. 

19 

93.61 

8.60 

93.57 

9.01 

93.53 

9.42 

94 

95 

94.64 

8. 

28 

94.60 

8.69 

94.56 

9.11 

94.52 

9.52 

95 

96 

95.63 

8. 

37 

95.60 

8.78 

95.56 

9.20 

95.52 

9.62 

96 

97 

96.63 

8. 

45 

96.59 

8.88 

96.55 

9.30 

96.51 

9.72 

97 

98 

97.63 

8. 

54 

97.59 

8.97 

97.55 

9.39 

97.51 

9.82 

98 

99 

98.62 

8. 

63 

98.59 

9.06 

98.54 

9.49 

98.50 

9.92 

99 

100 

99.62 

8. 

72 

99.58 

9.15 | 

99.54 

9 . 58 

99.50 

10.02 

100 

o 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

o 

o 

d 

• H 

Q 

85 Deg. 

84| Deg. 

1 

1 

84^ Deg. j 

1 

84£ Deg. 

e i 

CO 

• 

0 


20 







































































































14 


TRAVERSE TABLE. 


si 

s- ! 

6 Deg. 

6 } Deg. 

6 | Deg. 

6 ^ Deg. 

O 

ST 

<-► 

p 

P 

a 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lcit* 

Dep. 

Lat. 

Dep. 

P 

o 

9 

i 

0.99 

0.10 

0.99 

0.11 

0.99 

0.11 

0.99 

0.12 

i 

2 

1.99 

0.21 

1.99 

0.22 

1.99 

0.23 

1.99 

0.24 

9 

At 

. 3 

2.93 

0.31 

2.98 

0.33 

2.98 

0.34 

2.98 

0.35 

3 . 

4 

3.98 

0.41 

3.98 

0.44 

3.97 

0.45 

3.97 

0.47 

4 

5 

4.97 

0.52 

4.97 

0.54 

4.97 

0.57 

4.97 

0.59 

5 

/ 0 

5.97 

0.63 

5.96 

0.65 

5.96 

0.68 

5,96 

0.71 

6 

/ 7 

6.96 

0.73 

6.96 

0.76 

6.96 

0.79 

6.95 

0.82 

7 

[ 8 

7.96 

0.84 

7.95 

0.87 

7.95 

0.91 

7.94 

0.94 

8 

9 

3.95 

0.94 

8.95 

0.98 

8.94 

1.02 

8.94 

1.00 

9 

j 10 

9.95 

1.05 

9.94 

1.09 

9.94 

1.13 

9.93 

1.18 

10 

11 

30.94 

1.15 

10.93 

1.20 

10.93 

1.25 

10.92 

1.29 

11 

12 

11.93 

1 .25 

11.93 

1.31 

11.92 

1.36 

11.92 

1.41 

12 

13 

12.93 

1 .36 

12.92 

1.42 

12.92 

1.47 

12.91 

1.53 

13 

14 

13.92 

1.46 

13.92 

1.52 

13.91 

1.59 

13.90 

1.65 

14 

15 

14.92 

1.57 

14.91 

1.63 

14.90 

1 .70 

14.90 

1.76 

15 

10 

15.91 

1.67 

15.90 

1.74 

15.90 

1.81 

15.89 

1.88 

16 

17 

16.91 

1.78 

16.90 

1.85 

16.89 

1.92 

16.88 

2 00 

17 

18 

17.90 

1.88 

17.89 

1.96 

17.88 

2.04 

17.88 

2.12 

18 

19 

18.90 

1 .99 

18.89 

2.07 

18.88 

2.15 

18.87 

2.23 

19 

20 

19.S9 

2.09 

19.88 

2.18 

19.87 

2.26 

19.86 

2.35 

20 

21 

20.83 

2.20 

20.88 

2.29 

20.87 

2.38 

20.85 

2.47 

21 

22 

21.83 

2.30 

21 .87 

2.40 

21.86 

2.49 

21.85 

2.59 

22 

23 

22.87 

2.40 

22.88 

2.50 

22.85 

2.60 

22.84 

2.70 

23 

24 

23.87 

2.51 

23.86 

2.61 

23.85 

2.72 

,23.83 

2.82 

24 

25 

24.86 

2.61 j 

24.85 

2.72 

24.84 

2.83 

24.83 

2.94 

25 

26 

25.86 

2.72 

25.85 

2.83 

25.83 

2.94 

25.82 

3.06 

26 

27 

26.85 

2.82 

26.84 

2.94 

26.83 

3.06 

26.81 

3.17 

27 

28 

27.85 

2.93 

27.83 

3.05 

27.82 

3.17 

27.81 

3.29 

28 

29 

28.84 

3.03 

28.83 

3.16 

28.81 

3.28 

28.80 

3.41 

29 

30 

29.84 

3.14 

29.82 

3.27 

29.81 

3.40 

29.79 

3.53 

30 

31 

30.83 

3.24 

30.82 

3.37 

30.80 

3.51 

30.79 

3.64 

31 

32 

31 82 

3.34 

31.81 

3.48 

31.79 

3.62 

31.78 

3.76 

32 

33 

32.82 

3.45 

32.80 

3.59 

32.79 

3.74 

32.77 

3.88 

33 

34 

33.81 

3.55 

33.80 

3.70 

33.78 

3.85 

33.7G 

4.00 

34 

35 

34.81 

3.66 

34.79 

3.81 

34.78 

3.96 

34.76 

4.11 

35 

36 

35.80 

3.76 

35.79 

3.92 

35.77 

4.08 

35.75 

4.23 

'36 

37 

36.80 

3.87 

36.78 

4.03 

36.76 

4.19 

36.75 

4.35 

37 

33 

37.79 

3.97 

37.77 

4.14 

37.7ff 

4.30 

37.74 

4.47 

38 

39 

38.79 

4.08 

38.77 

4.25 

38.75 

4.41 

38.73 

4.58 

39 

40 

39.78 

4.18 

39.76 

4.35 

39.74 

4.53 

39.72 

4.70 

40 

41 

40.78 

4.29 

40.78 

4.46 

40.74 

4.64 

40.72 

4.82 

41 

42 

41.77 

4.39 

41.75 

4.57 

41.73 

4.76 

41.71 

4.94 

42 

43 

42.76 

4.49 

42.74 

4.68 

42.72 

4.87 

42.70 

5.05 

43 

44 

43.76 

4.60 

43.74 

4.79 

43.72 

4.98 

43.70 

5.17 

i 44 

45 

44.75 

4.70 

44.73 

4.90 

!44.71 

5.09 

44.69 

5.29 

45 

46 

45.75 

4.81 

45.73 

5.01 

45.70 

5.21 

45.68 

5.41 

46 

47 

46.74 

4.91 

46.72 

5.12 

46.70 

5.32 

46.07 

5.52 

47 

48 

47.74 

5.02 

47.71 

5.23 

47.69 

5.43 

47.67 

5.64 

48 

49 

48.73 

5.12 

48.71 

5.34 

48.69 

5.55 

48.06 

5.76 

49 

50 

49.73 

5.23 

49.70 

5.44 

49.68 

5.66 

49.65 

5.88 

50 

c 

o 

G 

Dap. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

o 

G 

C2 

*♦-» 

in 

' -H 

Q 

84 Deg. 

83f Deg. 

83^ 

Deg. 

83| Deg. 

a \ 

5 





























































































































TRAVERSE TABLE 


15 


o 
►— • 

a 

P 

6 Deg. 

6k Deg. 

6^ Deg 

61 Deg. 

Distance. 

3 

CJ 

© 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.72 

5.33 

50.70 

5.55 

50.67 

5.77 

50.65 

5.90 

51 

52 

51.72 

5.44 

51.69 

5.66 

51.67 

5-89 

51.64 

6.11 

52 

53 

52.71 

5.54 

52.68 

5.77 

52.66 

6.00 

52.63 

6.23 

53 

54 

53.70 

5.64 

53.68 

5.88 

53.65 

G-11 

53.63 

G. 35 

54 

55 

54.70 

5.75 

54.67 

5.99 

54.65 

6-23 

54.62 

6.46 

55 

50 

55.69 

5.85 

55.67 

6.10 

55.64 

6-34 

55.61 

6.58 

56 

57 

56.69 

5.96 

56.66 

6.21 

50.63 

6 • 45 

56.60 

0.70 

57 

53 

57.68 

6.06 

57.66 

6.31 

57.63 

6-57 

57.60 

6.82 

58 

59 

58.68 

6.17 

58.65 

6.42 

58.62 

6-68 

5S.59 

6.93 

59 

60 

59.67 

6.27 

59.64 

6.53 

59.61 

6-791 

59.58 

7.05 

60 

61 

60.67 

6.38 

60.64 

6.64 

60.01 

6.91 

60.58 

7.17 

61 

62 

61.66 

6.48 

61.63 

6.75 

61.60 

7.02 

61.57 

7.29 

62 

63 

62.65 

6.59 

62.63 

6.86 

62.60 

7. 13 | 

02 . 56 

7.40 

63 

64 

63.65 

6.69 

63.62 

6.97 

63.59 

7.25 | 

63 . 56 

7.52 

64 

65 

64.64 

6.79 | 

64.61 

7.08 

64.58 

7.36 j 

64.55 

7.64 

65 

66 

65 . 64 

6.90 

65.61 

7.19 

65 . 58 

7.47 1 

65.54 

7.76 

66 

67 

66.63 

7.00 

66.60 

7.29 

66.57 

7 58 1 

66.54 

7.88 

67 

68 

67.63 

7.11 

67.60 

7.40 

67.56 

7.70 

67.53 

7.99 

68 

69 

68.62 

7.21 1 

68.59 

7.51 

68 . 56 

7.81 

68.52 

8.11 

69 

70 

69.62 

7.32 i 

69.58 

7.02 

69.55 

7.92 

69.51 

8.23 

70 

71 

70.61 

7.42 

70 .58 

7.73 

70.54 

8.04 1 

70.51 

8.35 

71 

72 

71.61 

7.53 

71.57 

7.84 

71.54 

8.15 

71.50 

8.46 i 

72 

73 

72.60 

7.63 j 

72.57 

7.95 

72.53 

8.26 

72.49 

8.58 

73 

74 

73.59 

7.74 

73.56 

8.06 

73.52 

8.38 

73.49 

8.70 

74 

75 

74.59 

7.84 

74 . 55 

8.17 

74 . 52 

8.49 

.74.48 

8.82 

75 

76 

75 . 58 

7.84 

75.55 

8.27 

75 . 5 l 

8.60 

75.47 

8 . 93 

76 

77 

76 . 58 

8.05 1 

76 . 54 

8.38 

76 . 51 

S . 72 

76.47 

9 . 05 

77 

78 

77.57 

8.15 

77 . 54 

8.49 

77 . 50 

8.83 

77.46 

9.17 

78 

79 

78.57 

8.26 

78.53 

8.60 

78.49 

8.94 

78.45 

9.29 

79 

80 

79.56 

8.36 

79.53 

8.71 

79.49 

9.06 

79.45 

9.40 

80 

81 

80.56 

8.47 

80.52 

8.82 

80.48 

9.17 

80.44 

9 . 52 

81 

82 

81 . 55 

8.57 

81.51 

8.93 

81.47 

9.28 

81.43 

9 . 64 

82 

83 

82.55 

8.68 

82.51 

9.04 

82.47 

9.40 

:82 . 42 

9 . 76 

83 

84 

83 . 54 

8.78 

83.50 

9.14 

83.46 

9.51 

83.42 

9.87 

84 

85 

84.53 

8.88 

84.50 

9.25 

84.45 

9.62 

84.41 

9.99 

85 

86 

85.53 

8.99 

85.49 

9.36 

85.45 

9 . 74 

85.40 

10.11 

86 

87 

86.52 

9.09 

86.48 

9.47 

186.44 

9.85 

86.40 

10.23 

87 

88 

87.52 

9.20 

87.48 

9.58 

87.43 

9.96 

87.39 

10.34 

88 

89 

88.51 

9.30 I 

88.47 

9.69 

88.43 

10.08 

188.38 

10.46 

89 

90 

89.51 

9.41 1 

89.47 

9.80 

89.42 

10.19 

89.38 

10.53 

90 

91 

90.50 

9.51 

90.46 

9.91 

90.42 

10.30 

;90.57 

110.70 

91 

92 

91.50 

9.62 

91.45 

10.02 

91.41 

10.41 

1 91.36 

10.81 

92 

93 

92.49 

9.72 

92.45 

10.12 

92.40 

10.53 

192.36 

10.93 

93 

94 

93.49 

9.83 

93.44 

10.23 

93.40 

10.64 

!93.35 

11.05 

94 

95 

94.48 

9.93 

94.44 

10.31 

04.39 

10.75 

i94.34 

11.17 

95 

96 

95.47 

10.03 

95.43 

10.45 

95.38 

10.87 

|95.33 

1 1 .28 

i 96 

97 

96.47 

10.14 

96.42 

10.56 

96.38 

10.98 

I 96.33 

11.40 

97 

98 

97.46 

10.24 

97.42 

10.67 

97.37 

11.09 

97.32 

11 .52 

98 

99 

98.46 

10 . 35 

98.41 

10.78 

98.36 

11.21 

98.31 

11 . 64 

99 

100 

99.45 

10.46 

99.41 

10. SO 

99 . 36 

11 . 32 

99.31 

11 . 75 

100 

C 

o 

r-* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dop. 

Lat. 

1 Distance. 

i __ 

CO 

Q 

84 Deg. 

1 

831 Deg. 

831 

Deg. 

83| Deg. 


; 



















































































































16 


TRAVERSE TABLE. 


Distance. 

7 Deg. 

1\ Deg. 

71 Deg 

7$ Deg. 

| C 

V)' 

<-*■ 

p5 

Lat. 

Dep. 

Lat * 

D<sp. 

Lat* 

Dep. 

Lat. 

Dep. 

s 

p 

1 

0.99 

0.12 

0.99 

0.13 

0.99 

0.13 

0.99 

0.13 

] 

2 

1.99 

0.24 

1.98 

0.25 

1.98 

0.26 

1.98 

0.27 

2 

3 

2.98 

0.37 

2.98 

0.38 

2.97 

0.39 

2.97 

0.40 

3 

4 

3.97 

0.49 

3.97 

0.50 

3.97 

0.52 

3.96 

0.54 

4 

5 

4.96 

0.61 

4.96 

0.63 

4.96 

0.65 

4.95 

0.67 

5 

6 

5.96 

0.73 

5.95 

0.76 

5.95 

0.78 

5.95 

0.81 

6 

7 

6.95 

0.85 

6.94 

0.88 

6.94 

0.91 

6.94 

0.94 

7 

8 

7.94 

0.97 

7.94 

1.01 

7.93 

1.04 

7.93 

1.08 

8 

9 

8.93 

1.10 

8.93 

1.14 

8.92 

1.17 

8.92 

1.21 

9 

10 

9.93 

1.22 

9.92 

1.26 

9.91 

1.31 

9.91 

1.35 

10 

11 

10.92 

1.34 

10.91 

1.39 

10.91 

1.44 

10.90 

1.48 

11 

12 

11.91 

1.46 

11.90 

1.51 

11.90 

1.57 

11.89 

1.62 

12 

13 

12. GO 

1.58 

12.90 

1.64 

12.89 

1.70 

12.88 

1.75 

13 

14 

13.90 

1.71 

13.89 

1.77 

13.88 

1.83 

13.87 

1.89 

14 

15 

14.89 

1.83 

14.88 

1.89 

14.87 

1.96 

14.86 

2.02 

15 

16 

15.88 

1.95 

15.87 

2.02 

15.86 

2.09 

15.85 

2.16 

16 

17 

16.87 

2.07 

16.86 

2.15 

16.85 

2.22 

16.84 

2.29 

r/ 

18 

17.87 

2.19 

17.86 

2.27 

17.85 

2.35 

17.84 

2.43 

18 

19 

18.86 

2.32 

18.85 

2.40 

18.84 

2.48 

18.83 

2.56 

19 

20 

19.85 

2.44 

19.84 

2.52 

19.83 

2.61 

19.82 

2.70 

20 

21 

20.84 

2.56 

20.83 

2.65 

20.82 

2.74 

20.81 

2.83 

21 

22 

21.84 

2.68 

21.82 

2.78 

21.81 

2.87 

21.80 

2.97 

22 

23 

22.83 

2.80 

22.82 

2.90 

22.80 

3.00 

22.79 

3.10 

23 

24 

23.82 

2.92 

23.81 

3.03 

23.79 

3.13 

23.78 

3.24 

24 

25 

24.81 

3.05 

24.80 

3.15 

24.79 

3.26 

24.77 

3.37 

25 

26 

25.81 

3.17 

25.79 

3.28 

25.78 

3.39 

25.76 

3.51 

26 

27 

26.80 

3.29 

26.78 

3.41 

26.77 

3.52 

26.75 

3.64 

27 

28 

27.79 

3.41 

27.78 

3.53 

27.76 

3.65 

27.74 

3.78 

28 

29 

28.78 

3.53 

28.77 

3.66 

28.75 

3.79 

28.74 

3.91 

29 

30 

29.78 

3.66 

29.76 

3.79 

29.74 

3.92 

29.73 

4.05 

30 

31 

30.77 

3.78 

30.75 

3.91 

30.73 

4.05 

30.72 

4.18 

31 

32 

31.76 

3.90 

31.74 

4.04 

31.73 

4.18 

31.71 

4.32 

32 

33 

32.75 

4.02 

32.74 

4.16 

32.72 

4.31 

32.70 

4.45 

33 

34 

33.75 

4.14 

33.73 

4.29 

33.71 

4.44 

33.69 

4.58 

34 

35 

34.74 

4.27 

34 .72 

4.42 

34.70 

4.57 

34.68 

4.72 

35 

36 

35.73 

4.39 

35.71 

4.54 

35.69 

4.70 

35.67 

4.85 

36 

37 

36.72 

4.51 

36.70 

4.67 

36.68 

4.83 

36.66 

4.99 

37 

38 

37.72 

4.63 

37.70 

4.80 

37.67 

4.96 

37.65 

5.12 

38 

39 

38.71 

4.75 

38.69 

4.92 

38.67 

5.09 

38.64 

5.26 

39 

40 

39.70 

4.87 

39.68 

5.05 

39.66 

5.22 

39.63 

5.39 

40 

41 

40.70 

$.00 

40.67 

5.17 

40.65 

5.35 

40.63 

5.53 

41 

42 

41.69 

5.12 

41.66 

5.30 

41.64 

5.48 

41.62 

5.66 

42 

43 

42.68 

5.24 

42.66 

5.43 

42.63 

5.61 

42.61 

5.80 

43 

44 

43.67 

5.36 

43.65 

5.55 

43.62 

5.74 

43.60 

5.93 

44 

45 

44.67 

5.48 

44.64 

5.68 

44.62 

5.87 

44.59 

6.0 7 

45 

46 

45.66 

5.61 

45.63 

5.81 

45.61 

6.00 

45.58 

6.20 

46 

47 

46.65 

5.73 

46.62 

5.93 

46.60 

6.13 

46.57 

6.34 

47 

48 

47.64 

5.85 

47.62 

6.06 

47.59 

6.27 

47.56 

6.47 

48 

49 

48.63 

5.97 

48.61 

6.18 

48.58 

6.40 

48.55 

6.61 

49 

50 

49.63 

6.09 

49.60 

6.31 

49.57 

6.53 

49.54 

6.74 

50 

6 

V 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

o 

c 

d 

w 

• H 

Q 

83 Deg. 

82$ Deg. 

82J Deg. 

82$ Deg. 

c3 

+-> 

Cfl 

1 5 




































































































TRAVERSE TABLE. 


17 


o 

73 

c-* 

p 

7 Deg. 

7* Deg. 

U Deg. 

7| Deg. 

a 

GO* 

r"*> 

3 

O 

CO 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

•Lat. 

Dep. 

3 

O 

O 

51 

50.62 

6.22 

50.59 

6.44 

50.56 

6.66 

50.53 

6.83 

51 

52 

51.61 

6.34 

51.58 

6.56 

51.56 

6 .79 

51.53 

7.01 

52 

53 

52.60 

6.46 

52.58 

6.69 

52.55 

6.92 

52.52 

7.15 

53 

54 

53.60 

6.58 

53.57 

6.81 

53.54 

7.05 

53.51 

7.28 

54 

i 55 

54.59 

6 . 70 

54.56 

6.94 

54.53 

7.18 

54.50 

7.42 

55 

5 56 

55.58 

6.82 

55.55 

7.07 

55.52 

7.31 

55.49 

7.55 

56 

57 

56.53 

6.95 

56.54 

7.19 

58.51 

7.44 

56.48* 

7.69 

57 

58 

57.57 

7.07 

57.54 

7.32 

57.50 

7.57 

57.47 

7.82 

58 

59 

53.56 

7.19 

58.53 

7.45 

58.50 

7.70 

58.46 

7.96 1 

59 

60 

59.55 

7.31 

59.52 

7.57 

59.49 

7.83 

59.45 

8.09 1 

60 

61 

60.55 

7.43 

60.51 

7.70 

60.48 

7.96 

60.44 

8.23 

61 

62 

61.54 

7.56 

61.50 

7.82 

61.47 

8.09 

61.43 

8.36 

62 

63 

62.53 

7.68 

62.50 

7.95 

62.46 

8.22 

62.42 

8.50 

63 

64 

63.52 

7.80 

63.49 

8.08 

63.45 

8.35 

03.42 

8.63 

64 

65 

64.52 

7.92 

64.48 

8.20 

64.44 

8.48 

64.41 

8.77 

65 

66 

65.51 

8.04 

65.47 

8.33 

65.44 

8.61 

65.40 

8.90 

66 

67 

66 50 

8.17 

66.46 

8.46 

66.43 

8.75 

66.39 

9.04 

67 

68 

67.49 

8.29 

67.46 

8.58 

67.42 

8.88 

67.38 

9.17 

68 

69 

68.49 

8.41 

68.45 

8.71 

68.41 

9.01 

68.37 

9.30 

69 

70 

69.48 

8 .53 

69.44 

8.83 

69.40 

9.14 

69.36 

9.44 

70 

71 

70.47 

8.65 

70.43 

8.96 

70.39 

9.27 

70.35 

9.57 

71 

72 

71.46 

8.77 

71.42 

9.09 

71.38 

9.40 

71.34 

9.71 

72 

73 

72.46 

8.90 

72.42 

9.21 

72 33 

9.53 

72.33 

9.84 

73 

74 

73.45 

9.02 

73.41 

9.34 

73.37 

9.66 

73.32 

9.98 

74 

75 

74.44 

9.14 

74.40 

9.46 

74.36 

9.79 

74.31 

10.11 

75 

76 

75.43 

9.26 

75.39 

9.59 

75.35 

9.92 

75.31 

10.25 

76 

77 

76.43 

9.38 

76.38 

9.72 

76.34 

10.05 

76.30 

10.38 

77 

78 

77.42 

9.51 

77.38 

9.84 

77.33 

10.18 

77.29 

10.52 

I 78 

79 

78.41 

9.63 

78.37 

9.97 

78.32 

10.31 

78.28 

10.65 

79 

80 

79.40 

9.75 

79.36 

10.10 

79.32 

10.44 

79.27 

10.79 

80 

81 

80.40 

9.87 

80.35 

10.22 

'80.31 

10.57 

80.26 

10.92 

81 

82 

81.39 

9.99 

81.34 

10.35 

81.30 

10.70 

81.25 

11.06 

82 

83 

82.33 

10.12 

82.34 

10.47 

82.29 

10.83 

82.24 

11.19 

83 

84 

83.37 

10.24 

83.33 

10.60 

83.28 

10.96 

83.23 

11.33 

84 

85 

84.37 

10.36 

84.32 

10.73 

84.27 

11.09 

84.22 

11.40 

85 

86 

85.36 

10.48 

85.31 

10.85 

85.26 

11.23 

85.21 

11.60 

86 

87 

86.35 

10.60 

86.30 

10.98 

86.26 

11.36 

86.21 

11.73 

87 

88 

87.34 

10.72 

87.30 

11.11 

87.25 

11.49 

87.20 

11.87 

88 

89 

88.34 

10.85 

88.29 

11.23 

88.24 

11.62 

88.19 

12.00 

89 

90 

89.33 

10,97 

89.28 

11.36 

89.23 

11.75 

89.18 

12.14 

90 

91 

90.32 

11.09 

90.27 

11.48 

90.22 

11.88 

90.17 

12.27 

91 

92 

91.31 

11.21 

91.26 

11.61 

91.21 

12.01 

91.16 

12.41 

92 

93 

92.31 

11.33 

92.26 

11.74 

92.20 

12.14 

92.15 

12.54 

93 

94 

93.30 

11.46 

93.25 

11.86 

93.20 

12.27 

93.14 

12.68 

94 

95 

94.29 

11.58 

94.24 

11.99 

94.19 

12.40 

94.13 

12.81 

95 

96 

95.28 

11.70 

95.23 

12.12 

95.18 

12.53 

95.12 

12.95 

96 

97 

96.28 

11.82 

96.22 

12.24 

96.17 

12.66 

96.11 

13.08 

97 

93 

97.27 

11.94 

97.22 

12.37 

97.16 

12.79 

97.10 

13.22 

93 

99 

93.26 

12.07 

98.21 

12.49 

93.15 

12.92 

93.10 

13.35 

99 

100 

99.25 

12.19 

99.20 

12.62 

99.14 

13.05 

99.09 

13.49 

100 

c> 

o 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

P 

a 

CO 

83 Deg. 

82f Deg. 

821 

Deg. 

82J Deg. 

d 

SO 

C 








































































































18 


TRAVERSE TABLE. 


! - 

s 

to 

8 Deg. 

8 } Deg. 

Q-h Deg. 

8 } Deg. 

o 

to 

P 

P 

o 

O 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

n 

a 

1 

0.99 

0.14 

0.99 

0.14 

0.99 

0.15 

0.99 

0.15 

i 

2 

1.98 

0.28 

1 .9S 

0.29 

1.98 

0.30 

1.98 

0.30 

2 

3 

2.07 

0.42 

2.97 

0.43 

2.97 

0.44 

2.97 

0.46 

o 

o 

4 

3.96 

0.56 

3.96 

0.57 

3.96 

0.59 

3.95 

0.61 

A 

5 

4.95 

0.70 

4.95 

0.72 

4.95 

0.74 

4.94 

0.76 

5 5 

6 

5.94 

0.84 

5.94 

0.86 

5.93 

0.89 

5.93 

0 91 

6 

7 

6 .93i 

0.97 

6.93 

1.00 

6.92 

1.03 

6.92 

1,06 

7 

8 

7.92* 

1 . 11 

7.92 

1.15 

7.91 

1.18 

7.91 

1 22 

8 

9 

8.91 

1.25 

8.91 

1.29 

8.90 

1.33 

8.90 

1.37 

9 

10 

9.90 

1.39 

9.90 

1.43 

9.89 

1.48 

9.88 

1.52 

10 

11 

10.89 

1.53 

10.89 

1.53 

10.88 

1.63 

10.87 

1.67 

11 

12 

11.88 

1.67 

11.88 

1.72 

11.87 

1.77 

11.86 

1 .S3 

12 

13 

12.87 

1.81 

12.87 

1.87 

12.86 

1.92 

12.85 

I .93 

13 

14 

13.88 

1.95 

13.86 

2.01 

13.85 

2.07 

13.84 

2.13 

14 

15 

14.85 

2.09 

14.85 

2.15 

14.84 

on 

** • ■<«/ rW 

14.83 

2.28 

15 

16 

15.84 

2.23 

15.84 

2.30 

15.82 

2.36 

15.81 

2.43 

16 

17 

16.83 

2.37 

16.83 

2.44 

16.81 

2.51 | 

16.80 

2.59 

17 

IS 

17.82 

2.51 

17.81 

2.58 

17.80 

2.66 

17.79 

2.74 

18 

19 

18.82 

2.64 

IS. SO 

2.73 

18.79 

2.81 

13.78 

2.89 

19 

20 

19.81 

2.78 

19.79 

2.87 | 

19.78 

2.96 

19.77 

3.04 

20 

21 

20.80 

o no 

20.78 

3.0 L 

20.77 

3.10 ! 

20.76 

3. 19 

21 

22 

2! . 79 

3.06 

21.77 

3.16 j 

21.76 

3.25 

21.74 

3.35 

22 

23 

22.78 

3.20 

22.76 

3.39 

22.75 

3.40 

22.73 

3.50 

23 

24 

23.77 

3.34 

23.75 

3.44 1 

23.74 

3.55 

23.72 

3.65 

24 

25 

24.76 

3.48 

24.74 

3.59 

24.73 

3.70 

24.71 

3.80 

25 

20 

25.75 

3.62 

25.73 

3.73 

25.71 

3.84 

125.70 

3.98 

26 

27 

26.74 

3.76 

28.72 

3.87 

26.70 

3.99 | 

126.69 

4.11 

27 

28 

27.73 

3.90 

27.71 

4.02 

27.69 

4.14 ! 

127.67 

4.26 

23 

29 

28.72 

4.04 

28.70 

4.16 

28.68 

4.29 

!28.66 

4.41 

29 

30 

29.71 

4.18 

29.69 

4.30 

29.67 

4.43 

29.65 

4.56 

30 

ITT 

30.70 

4.31 

30.68 

4.45 

30.66 

4.58 

!30.64 

4.72 

31 

32 

31.69 

4.45 

31.67 

4.59 

31.65 

4.73 

31.63 

4.87 

32 

33 

32.88 

4.59 

32.66 

4.74 

32.64 

4.88 

32.62 

5.02 

33 

34 

33.67 

4.73 

33.65 

4.88 

33.63 

5.03 

j33.60 

5.17 

34 

35 

34.66 

4.87 

34.64 

5.02 

34.62 

5.17 

34.59 

5.32 

35 

36 

35.65 

5.01 

35.63 

5.17 

35.60 

5.32 

35.58 

5.48 

36 

37 

38.64 

5.15 

36.62 

•5.31 

36.59 

5.47 

38.57 

5.63 

37 

38 

37.63 

5.29 

37.61 

5.45 

37.58 

5.62 

37.56 

5.78 

33 

39 

38.62 

5.43 

38.60 

5.60 

33.57 

5.76 

33.55 

5.93 

39 

40 

39.61 

5.57 

39-59 

5.74 

39.56 

5.91 

35.53 

6.08 

40 

41 

40.60 

5.71 

40.58 

5.88 

40.55 

6.06 

40.52 

6.24 

41 

42 

41.59 

5.85 

41.57 

6.03 

41.54 

6.21 

41.51 

6.39 

42 

43 

42.58 

5.98 

42.56 

6.17 

42.53 

6.36 

42.50 

6.54 

43 

44 

43.57 

6.12 

43.54 

6.31 

43.52 

6.50 

43.49 

6.69 

44 

45 

44.56 

6.26 

44.53 

6.46 

44.51 

6.65 

144.48 

6.85 

45 

46 

45.55 

6.40 

45.52 

6.60 

45.49 

6.80 

45.46 

7.00 

46 

47 

46.54 

6.54 

46.51 

6.74 

46.48 

6.95 

:46.45 

7.15 

47 

48 

47.53 

6.68 

47.50 

6.89 

47.47 

7.09 

i47.44 

7.30 

43 

49 

48.52 

6.82 

48.49 

7.03 

48.46 

7.24 

48.43 

7.45 

49 

50 

49.51 

6.96 

49.48 

7.17 

49.45 

7.39 

49.42 

7.61 

50 

V 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

i—l 

ci 

+-> 

to 

• 

Q 

82 Deg. 

Clf 

Deg. 

81g- 

Dog. 

81} Deg-. 

rt 

to 

P 












































































































TRAVERSE TABLE 


19 


Distance. J 

8 Deg. 

8 ,} Deg. 

| 

H Deg. 

8 | Dog. 

Distance. 

Lat. 

i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.50 

7.10 

50.47 

7.32 

50.44 

7.54 

50.41 

7. 

76 

51 

52 

51.49 

7.24 

51.46 

7.46 

51.43 

7.69 

51.39 

7. 

91 

52 

53 

52.48 

7.33 

52.45 

7.61 

52.42 

7.83 

52.38' 

8 . 

06 

53 

54 

53.47 

7.52 

53.44 

7.75 

53.41 

7.98 

53.37 

8 . 

21 

• 54 

55 

54.46 

7.65 

54.43 

7.89 

54.40 

8.13 

54.36 

8 . 

37 

55 

5G 

55.48 

7.79 

55.42 

8.04 

55.38 

8.28 

55.35 

8 . 

52 

56 

57 

56.45 

7.93 

56.41 

8.18 

56.37 

8.43 

56.34 

8 . 

67 

57 

58 

57.44 

8.07 

57.40 

8.32 

57.36 

8.57 

57.32’- 

8 . 

82 

58 

59 

58.43 

8.21 

58.39 

8.47 

58.35 

8.72 

58.31 

8 . 

98 

59 

| 60 

59.42 

8.35 

59-38 

8.-61 

59.34 

8.87 

59.30 

9. 

13 

60 

61 

60.41 

8.49 

60.37 

8 .75 

60.33 

9.02 

60.29 

9. 

28 

61 

62 

61.40 

8.63 

61.36 

8.90 

61.32 

9.16 

61.28 

9. 

43 

62 

63 

62.39 

8.77 

62.35 

9.04 

62.31 

9.31 

62.27 

9. 

58 

63 

64 

63.38 

8.91 

63.34 

9.18 

63.30 

9.46 

63.26 

9. 

74 

64 

65 

64.37 

9.05 

64.33 

9.33 

64.29 

9.61 

64.24 

9. 

89 

65 

66 

65.36 

9.19 

65.32 

9.47 

65.28 

9.76 

65.23 

10 . 

04 

66 

87 

66.35 

9.32 

66.31 

9.61 

66.26 

9.90 

66.22 

10 . 

19 

67 

63 

67.34 

9.46 

67.30 

9.76 

67.25 

10.05 

67.21 

10 . 

34 

68 

69 

68.33 

9.60 

68.29 

9.90 

68.24 

10.20 

68.20 

10 . 

50 

69 

70 

69.32 

9.74 

69.28 

10.04 

69.23 

10.35 

69.19 

10 . 

65 

70 

71 

70.31 

9.88 

70.27 

10.19 

70.22 

10.49 

70.17 

10 . 

80 

71 

72 

71.30 

10.02 

71.25 

10.33 

71.21 

10.64 

71.16 

10 . 

95 

72 

73 

72.29 

10.16 

72.24 

10.47 

72.20 

10.79 

72.15 

11 . 

10 

73 

74 

73.28 

10.30 

73.23 

10.62 

73.19 

10.94 

73.14 

11 . 

26 

74 

75 

74.27 

10.44 

74.22 

10.76 

74.18 

11.09 

74.13 

] 1 

41 

75 

76 

75.26 

10.58 

75.21 

10.91 

75.17 

11.23 

75.12 

11 

56 

76 

/ / 

76.25 

10.72 

76.20 

11.05 

76.15 

11.38 

76.10 

u 

71 

77 

78 

77.24 

10 .S6 

77.19 

11.19 

77.14 

11.53 

77.09 

11 

87 

78 

79 

78.23 

10.99 

78.18 

11.34 

78.13 

11.68 

78.08 

12 

.02 

79 

80 

79.22 

11.13 

79.17 

11.48 

79.12 

11.82 

79.07 

12 

.17 

80 

81 

80.21 

11.27 

80.16 

11.62 

80.11 

11.97 

80.06 

12 

.32 

81 

82 

81.20 

11.41 

81.15 

11.77 

81.10 

12.12 

81.05 

12 

.47 

82 

83 

82.19 

11.55 

82.14 

11.91 

82.09 

12.27 

82.03 

12 

.63 

83 

84 

83.18 

11.69 

83.13 

12.05 

83.08 

12.42 

83.02 

12 

.78 

84 

85 

84.17 

11.83 

84.12 

12.20 

84.07 

12.56 

84.01 

12 

.93 

85 

86 

85.16 

11.97 

85.11 

12.34 

85.06 

12.71 

85.00 

13 

.08 

86 

87 

86.15 

12.11 

86.10 

12.48 

86.04 

12.86 

85.99 

13 

.23 

87 

88 

87.14 

12.25 

87.09 

12.63 

87.03 

13.01 

86.98 

13 

.39 

88 

89 

88.13 

12.39 

88.08 

12.77 

88.02 

13.16 

87.96 

13 

.54 

89 

90 

89.12 

12.53 

89.07 

12.91 

89.01 

13.30 

88.95 

13 

.69 

90 

91 

90.11 

12.66 

90.06 

13.06 

90.00 

13.45 

89.94 

13 

.84 

91 

92 

91.10 

12.80 

91.05 

13.20 

90.99 

13.60 

90.93 

14 

.00 

92 

93 

92.09 

12.94 

92.04 

13.34 

91.98 

13.75 

91.92 

14 

.15 

93 

94 

93.09 

13.08 

93.03 

13.49 

92.97 

13.89 

92.91 

14 

.30 

94 

95 

94. OS 

13.22 

i94.02 

13.63 

i93.96 

14.04 

93.89 

14 

.45 

95 

96 

95.07 

13.36 

95.01 

13.78 

94.95 

14.19 

94.88 

14 

.60 

96 

97 

96.08 

13.50 

96.00 

13.92 

195.93 

14.34 

95.87 

14 

. 76 

97 

98 

97.05 

13.64 

96.99 

14.06 

96.92 

14.49 

96.86 

14 

.91 

98 

99 

98.04 

13.78 

97.98 

14.21 

97.91 

14.63 

97.85 

15 

. 06 

99 

100 

99.03 

13.92 

98.97 

14.35 

93.90 

14.78 

98.84 

15 

.21 

100 

CD 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

| Distance. 

ci 

IQ 

5 

| 82 Dog. 

81J Deg. 

8 H Deg. 

81^ Deg. 











































































































20 


TRAVERSE TABLE 


O 
>— • 

rji 

r+ 

P2 

3 

O 

P 

9 Deg. 

9} Deg, 

9| Deg. 

9.} Deg 

Distance. J 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.99 

0.16 

0.99 

0.16 

0.99 

0.17 

0.99 

0.17 

1 

2 

1.98 

0.31 

1.97 

0.32 

1.97 

0.33 

1.97 

0.34 

2 

3 

2.96 

0.47 

2.96 

0.48 

2.96 

0.50 

2.96 

0.51 

3 

4 

3.95 

0.63 

3.95 

0.64 

3.95 

0.66 

3.94 

0.68 

4 

5 

4.94 

0.78 

4.93 

0.80 

4.93 

0.83 

4.93 

0.85 

5 

6 

5.93 

0.94 

5.92 

0.96 

5.92 

0.99 

5.91 

1.02 

6 

7 

6.91 

1.10 

6.91 

1.13 

6.90 

1.16 

6.90 

1.19 

7 

8 

7.90 

1.25 

7.90 

1.29 

7.89 

1.32 

7.88 

1.35 

8 

9 

8.89 

1.41 

8.88 

1.45 

8.88 

1.49 

8.87 

1.52 

9 

10 

9.8S 

1.56 

9.87 

1.61 

9.86 

1.65 

9.86 

1.69 

10 

11 

10.86 

1.72 

10.86 

1.77 

10.85 

1.82 

10.84 

1.86 

11 

12 

11.85 

1.88 

11.84 

1.93 

11.84 

1.98 

11.83 

2.03 

12 

13 

12.84 

2.03 

12.83 

2.09 

12.82 

2.15 

12.81 

2.20 

13 

14 

13.83 

2.19 

13.82 

2.25 

13.81 

2.31 

13.80 

2,37 

14 

15 

14.82 

2.35 

14.80 

2.41 

14.79 

2.48 

14.78 

2.54 

15 

16 

15.80 

2.50 

15.79 

2.57 

15.78 

2.64 

15.77 

2.71 

16 

17 

16.79 

2.66 

16.78 

2.73 

16.77 

2.81 

16.75 

2.88 

17 

18 

17.78 

2.82 

17.77 

2.89 

17.75 

2.97 

17.74 

3.05 

IS 

19 

18.77 

2.97 

18.75 

3.05 

18.74 

3.14 

18.73 

3.22 

19 

20 

19.75 

3.13 

19.74 

3.21 

19.73 

3.30 

19.71 

3.39 

20 

21 

20.74 

3.29 ; 

20.73 

3.33 

20.71 

3.47 

20.70 

3.56 

21 

22 

21.73 

3.44 

21.71 

3.54 

21.70 

3.63 

21.68 

3.73 

22 

23 

22.72 

3.60 ; 

22.70 

3.70 

22.68 

3.80 

22.67 

3.90 

23 

24 

23.70 

3.75 

23.69 

3.86 

23.87 

3.96 

23.65 

4.06 

24 

25 

24.69 

3.91 

24.67 

4.02 

24.68 

4.13 

24.64 

4.23 

25 

26 

25.68 

4.07 

25.66 

4.18 

25.64 

4.29 

25.62 

4.40 

26 

27 

26.67 

4.22 

26.65 

4.34 

26.63 

4.46 

26.61 

4.57 

27 

28 

27.66 

4.38 

27.64 

4.50 

27.62 

4.62 

27.60 

4.74 

28 

29 

28.64 

4.54 

28.62 

4.66 

28.60 

4.79 

28.58 

4.91 

29 

30 

29.63 

4.69 

29.61 

4.82 

29.59 

4.95 

29.57 

5.08 

30 

3 L 

30.62 

4.85 

30.80 

4.98 

30.57 

5.12 

30.55 

5.25 

31 

32 

31.61 

5.01 

31.58 

5.14 

31.56 

5.28 

31.54 

5.42 

32 

33 

32.59 

5.16 

32.57 

5.30 

32.55 

5.45 

32.52 

5.59 

33 

34 

33.58 

5.32 

33.56 

5.47 

33.53 

5.61 

33.51 

5.76 

34 

35 

34.57 

5.48 

34.54 

5.63 

34.52 

5.78 

34.49 

5.93 

35 

36 

35.56 

5.63 

35.53 

5.79 

35.51 

5.94 

35.48 

6.10 

36 

37 

36.54 

5.79 

36.52 

5.95 

36.49 

6.11 

36.47 

6.27 

37 

38 

37.53 

5.94 

37.51 

6.11 

37.48 

6.27 

37.45 

6.44 

38 

39 

38.52 

6.10 

38.49 

6.27 

38.47 

6.44 

38.44 

6.60 

39 

40 

39.51 

6.26 

39.48 

6.43 

39.45 

6.60 

39.42 

6.77 

40 

41 

40.50 

6.41 

40.47 

6.59 

40.44 

6.77 

40.41 

6.94 

41 

42 

41.48 

6.57 

41.45 

6.75 

41.42 

6.92 

41.39 

7.11 

42 

43 

42.47 

6.73 

42.44 

6.91 

42.41 

7.10 

42.38 

7.28 

43 

44 

43.46 

6.88 

43.43 

7.07 

43.40 

7.26 

43.36 

7.45 

44 

45 

44.45 

7.04 

44.41 

7.23 

44.38 

7.43 

44.35 

7.62 

45 

46 

45.43 

7.20 

45.40 

7.39 

45.37 

7.59 

45.34 

7.79 

46 

47 

46.42 

7.35 

46.39 

7.55 

46.36 

7.76 

46.32 

7.96 

47 

48 

47.41 

7.51 

47.38 

7.72 

47.34 

7.92 

47.31 

8.13 

48 

49 

48.40 

7.67 

48.36 

7.88 

48.33 

8.09 

48.29 

8.30 

49 

50 

49.38 

7.82 

49.35 

8.04 

49.32 

8.25 

49.28 

8.47 

50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

V 

o 

a 

03 

• H 

ft 

81 Deg. 

80f Deg. 

801 

Deg. 

80} Deg. 


































































































TUAVEKSE TABLE. 


21 


Distance.! 

9 Deg. 

I 

n Deg. 


91 Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.37 

7.98 

50.34 

8.20 

50.30 

8.42 

50.26 

8.64 

51 

52 

51.36 

8.13 

51.32 

8.36 

51.29 

8.58 

51.25 

8.81 

52 

53 

52.35 

8.29 

52.31 

8.52 

j 52.27 

8.75 

52.23 

8.98 

53 

54 

53.34 

8.45 

53.30 

8.68 

53.26 

8.91 

53.22 

9.14 

54 

55 

54.32 

8.60 

54.28 

8.84 

54.25 

9.03 

54.21 

9.31 

55 

56 

55.31 

8.76 

55.27 

9.00 

55.23 

9.24 

55.19 

9.48 

56 

57 

56.30 

8.92 

56.26 

9.16 

56.22 

9.41 

56.18 

9.65 

57 

58 

57.29 

9.07 

57.25 

9.32 

57.20 

9.57 

57.16 

9.82 

58 

59 

58.27 

9.23 

58.23 

9.48 

58.19 

9.74 

58.15 

9.99 

59 

GO 

59.26 

9.39 

59.22 

9.64 

59.18 

9.90 

59.13 

10.16 

60 

61 

60.25 

9.54 

60.21 

9.81 

60.16 

10.07 

60.12 

10.33 

61 

62 

61.24 

9.70 

61.19 

9.97 

61.15 

10.23 

61.10 

10.50 

62 

63 

62.22 

9.86 

62.18 

10.13 

62.14 

10.40 

62'.09 

10.67 

63 

64 

63.21 

10.01 

63.17 

10.29 

63.12 

10.56 

63.08 

10.84 

64 

65 

64.20 

10.17 

64.15 

10.45 

64.11 

10.73 

64.06 

11.01 

65 

66 

65.19 

10.32 

65.14 

10.61 

65.09 

10.89 

65.05 

11.18 

66 

67 

66.18 

10.48 

66.13 

10.77 

66.08 

11.06 

66.03 

11 .35 

67 

68 

67.16 

10.64 

67.12 

10.93 

67.07 

11.22 

67.02 

11.52 

68 

69 

68.15 

10.79 

68.10 

11.09 

68.05 

11.39 

68.00 

11.69 

69 

70 

69.14 

10.95 

69.09 

11.25 

69.04 

11.55 

68.99 

11.85 

70 

71 

70.13 

11.11 

70.08 

11.41 

70.03 

11.72 

69.97 

12.02 

71 

72 

71.11 

11.26 

71.06 

11.57 

71.01 

11.88 

70.96 

12.19 

72 

73 

72.10 

11.42 

72.05 

11.73 

72.00 

12.05 

71.95 

12.36 

73 

74 

73.09 

11.58 

73.04 

11.89 

72.99 

12.21 

72.93 

12.53 

74 

75 

74.08 

11.73 

74.02 

12.06 

73.97 

12.38 

i73.92 

12.70 

75 

76 

75.06 

11.89 

75.01 

12.22 

74.96 

12.54 

74.90 

12.87 

76 

77 

76.05 

12.05 

76.00 

12.38 

75.94 

12.71 

75.89 

13.04 

77 

78 

77.04 

12.20 

76.99 

12.54 

76.93 

12.87 

76.87 

13.21 

78 

79 

78.03 

12.36 

77.97 

12.70 

77.92 

13.04 

77.86 

13.38 

79 

80 

79.02 

12.51 

78.96 

12.86 

78.90 

13.20 

I78.84 

13.55 

80 

81 

80.00 

12.67 

79.95 

13.02 

79.89 

13.37 

79.83 

13.72 

81 

82 

80.99 

12.83 

80.93 

13.18 

80.88 

13.53 

80.82 

13.89 

82 

83 

81.98 

12.98 

81.92 

13.34 

81.86 

13.70 

81.80 

14.06 

83 

84 

82.97 

13.14 

82.91 

13.50 

82.85 

13.86 

I 82.79 

14.23 

84 

85 

83.95 

13.30 

83.89 

13.66 

83.83 

14.03 

83.77 

14.39 

85 

86 

84.94 

13.45 

84.88 

13.82 

84.82 

14.19 

84.76 

14.56 

86 

87 

85.93 

13.61 

85.87 

13.98 

85.81 

14.36 

85.74 

14.73 

87 

88 

86.92 

13.77 

86.86 

14.15 

86.79 

14.52 

86.73 

14.90 

88 

89 

87.90 

13.92 

87.84 

14.31 

87.78 

14.69 

87.71 

15.07 

89 

90 

88.89 

14.08 

88.83 

14.47 

88.77 

14.85 

88.70 

15.24 

90 

91 

89.88 

14.24 

89.82 

14.63 

89.75 

15.02 

89.69 

15.41 

91 

92 

90.87 

14.39 

90.80 

14.79 

90.74 

15.18 

90.67 

15.58 

92 

93 

91.86 

14.55 

91.79 

14.95 

91.72 

15.35 

91.66 

15.75 

93 

94 

92.84 

14.70 

92.78 

15.11 

92.71 

15.51 

92.64 

15.92 

94 

95 

93.83 

14.86 

93.76 

15.27 

93.70 

15.68 

93.63 

16.09 

95 

96 

94.82 

15.02 

94.75 

15.43 

94.68 

15.84 

94.61 

16.26 

96 

97 

95.81 

15.17 

95.74 

15.59 

95.67 

16.01 

95.60 

16 43 

97 

98 

96.79 

15.33 

96.73 

15.75 

96.66 

16.17 

96.58 

16.60 

98 

99 

97.78 

15.49 

97.71 

15.91 

97.64 

16.34 

97.57 

16.77 

99 

100 

98.77 

15.64 

98.70 

16.07 

98.63 

16.50 

98.56 

16.93 

100 

o 

o 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o’ 

o 

c 

ci 
+-> 
in 
• —» 

p 

81 Deg. 

80f Deg. 

80^ Deg. 

801 Deg. 

cd 

C/l 

• — A 

Q 








































































































22 


TRAVERSE TABLE 


a 

k— • 

73 

(-*■ 

P 

o 

a 

• 

10 Deg. 

10} Deg. 

10} 

1 

Deg. 

1 

lOf Deg. 

Distance.J 


Dep. 

Lat. 

Dep. 

L/&t» 

Dep. 

Lat. 

Dep. 

i 

0.98 

0.17 

0.98 

0.18 

0.98 

0.18 

0.98 

0.19 

1 

2 

1.97 

0.35 

1,97 

0.36 

1.97 

0.36 

1.96 

0.37 

2 

3 

2.95 

0.52 

2.95 

0.53 

2.95 

0.55 

2.95 

0 56 

3 

4 

3.94 

0.69 

3.94 

0.71 

3.93 

0.73 

3.93 

0.75 

4 

5 

4.92 

0.87 

4.92 

0.89 

4.92 

0.91 

4.91 

0.93 

5 

6 

5.91 

1 .04 

5.90 

1.07 

5.90 

1.09 

5.89 

1 ■ 12 

0 

7 

6.89 

1.22 

6.89 

1.25 

6.88 

1.28 

6.88 

1.31 

7 

8 

7.88 

1.39 

7.87 

1.42 

7.87 

1.46 

7.86 

1.49 

8 

9 

8.86 

1.56 

8.86 

1.60 

8.85 

1.64 

8.84 

1.68 

9 

10 

9.85 

1.74 

9.84 

1.78 

9.83 

1.82 

9.82 

1.87 

10 

11 

10.83 

J .91 

10.82 

1.98 

10.82 

2.00 

10.81 

2.05 

11 

12 

11.82 

2. OS 

11.81 

2.14 

11.80 

2.19 

11.79 

2.24 

12 

13 

12.80 

2.26 

12.79 

2.31 

12.78 

2.37 

12.77 

2.42 

13 

14 

13.79 

2.43 1 

13.78 

2.49 

13.77 

2.55 

13.75 

2.61 

14 

15 

14.77 

2.60 

14.76 

2.67 

14.75 

2.73 

14.74 

2.80 

15 

16 

15.76 

2.78 

15.74 

2.85 1 

15.73 

2.92 

15.72 

2.98 

16 

17 

16.74 

2.95 

16.73 

3.03 

16.72 

3.10 

16.70 

3.17 

17 

18 

17.73 

3.13 

17.71 

3.20 

17.70 

3.28 

17.68 

3.36 

18 

19 

IS.71 

3.30 

18.70 

3.38 

18.68 

3.46 

18.67 

3.54 

19 

20 

19.70 

3.47 

19.68 

3.50 

19.67 

3.64 

19.65 

3.73 

20 

21 

20.68 

3.65 

20.66 

3.74 

20.65 

3.83 

20.63 

3.92 

21 

22 

21.67 

3.82 

21.65 

3.91 

21.63 

4.01 

21.61 

4.10 

99 

Ar />V 

23 

22.65 

3.99 

22.63 

4.09 

22.61 

4.19 

22.60 

4.29 

23 

24 

23.64 

4.17 

23.62 

4.27 

23.60 

4.37 

23.58 

4.48 

24 

25 

24.62 

4 >34 

24.60 

4.45 

24.58 

4.56 

24.56 

4.66 

25 

26 

25.61 

4.51 

25.59 

4.63 

25.56 

4.74 

25.54 

4.85 

26 

27 

26.59 

4.69 

26.57 

4.80 1 

26.55 

4.92 

26.53 

5.04 

27 

28 

27.57 

4.66 

27.55 

4.93 

27.53 

5.10 

27.51 

5.22 

28 

29 

28.56 

5.04 

28.54 

5.16 

28.51 

5.28 

28.49 

5.41 

29 

30 

29.54 

5.21 

29.52 

5.34 

29.50 

5.47 

29.47 

5.60 

30 

31 

30.53 

5.38 

30.51 

5.52 ! 

30.48 

5.65 

30.46 

5.78 

31 

32 

31.51 

5.56 

31.49 

5.69 

31.46 

5.83 

31.44 

5.97 

32 

33 

32.50 

5.73 

32.47 

5.87 

32.45 

6.01 

32.42 

6.16 

33 

34 

33.48 

5.90 

33.46 

6.05 

33.43 

6.20 

33.40 

6.34 

34 

35 

34.47 

6.08 

34.44 

6.23 

34.41 

6.38 

34.39 

6.53 

35 

36 

35.45 

6.25 

35.43 

6.41 

35.40 

6.56 

35.37 

6.71 

36 

37 

36.44 

6.42 

36.41 

6.58 

36.38 

6.74 

36.35 

6.90 

37 

38 

37.42 

6.60 

37.39 

6.76 

37.36 

0.92 

37.33 

7.09 

38 

39 

38.41 

6.77 

38.38 

6.94 

38.35 

7.11 

38.32 

7.27 

39 

40 

39.39 

6.95 

39.36 

7.12 

39.33 

7.29 

39.30 

7.46 

40 

41 

40.38 

7.12 

40.35 

7.30 

40.31 

7.47 

40.28 

7.65 

41 

42 

41.36 

7.29 

41.33 

7.47 

41.30 

7.65 

41.26 

7.83 

42 

43 

42.35 

7.47 

42.31 

7.65 

42.28 

7.84 

42.25 

8.02 

43 

44 

43.33 

7.64 

43.30 

7.83 

43.26 

8.02 

43.23 

8.21 

44 

45 

44.32 

7.81 

44.28 

8.01 

44.25 

8.20 

44.21 

8.39 

45 

46 

45.30 

7.99 

45.27 

8.19 

45.23 

8.38 

45.19 

8.58 

46 

47 

46.29 

8.16 

[46.25 

8.36 

46.21 

8.57 

46.18 

8.77 

47 

48 

47.27 

8.34 

47.23 

8.54 

47.20 

8.75 

47.16 

8.95 

48 

49 

48.26 

I 8.51 

48.22 

8.72 

48.18 

8.93 

48.14 

9.14 

49 

50 

I49.24 

8.68 

49.20 

8.90 

49.16 

9.11 

49.12 

9.33 

50 

• 

O 

o 

c 

d 

*-> 

c/s 

r 

Dep. 

| Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

| Distance. | 

80 Deg. 

79.| Deg. 

79‘- Deg. 

79} Deg. 

























































































TEAVERSE TABLE. 


23 


Distance, j 

10 Deg. 

101 Deg. 

l°i 

i 

Deg. 

lOf Deg. 

Distance. 

Jf 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.23 

8.86 

50.19 

9.08 

50.15 

9.29 

50.10 

9.51 

51 

52 

51.21 

9.03 

51.17 

9.25 

51:13 

9.48 

51.09 

9.70 

52 

53 

52.19 

9.20 

52.15 

9.43 

52.11 

9.66 

52.07 

9.89 

53 1 

54 

53.18 | 

9.38 

53.14 

9.61 

53.10 

9.84 

53.05 

10.07 

54 

55 

54.16 

9.55 

54.12 

9.79 

54.08 

10.02 

54.03 

10.26 

55 

50 

55.15 

9.72 

55.11 

9.96 

55.06 

10.21 

55.02 

10.45 

56 j 

57 

56.13 

9.90 

56.09 

10.14 

56.05 

10.39 

56.00 

10.63 

57 | 

58 

57.12 

10.07 

57.07 

10.32 

57.03 

10.57 

56.98 

10.82 

58 

59 

58.10 

10.25 

58.06 ! 

10.50 

58.01 

10.75 

57.96 

11.00 

59 

69 

59.09 ! 

10.42 

59.04 

10.68 

59.00 

10.93 

58.95 

11.19 

60 

61 i 

60.07 ; 

10.59 

60.03 

10.85 

59.98 

11.12 

59.93 

11.38 

61 

62 

61.06 j 

10.77 

61.01 

11.03 

60.96 

11.30 

60.91 

11.56 

62 

63 

62.04 

10.94 

61.99 

31.21 

61.95 

11.48 

61.89 

11.75 

63 

64 

63.03 i 

11*11 

62.98 

11.39 

62.93 

11.66 

62.88 

11.94 I 

64 

65 

64.01 

11.29 

63.96 

11.57 

63.91 

11.85 

63.86 

12.12 

65 

66 

65.00 

11.46 

64.95 

11.74 

64.89 

12.03 

64.84 

12.31 

66 

67 

65.98 

11.63 

65.93 

11.92 

65.88 

12.21 

65.82 

12.50 

67 

68 

66.97 

11.81 

66.91 

12.10 

66.88 

12.39 

66.81 

12.68 

68 

69 

67.95 

11.98 

67.90 

12.28 

67.84 

12.57 

67.79 

12.87 

69 

70 

08.94 

12.16 

68.88 

12.46 

68.83 

12.76 

68.77 

13.06 

70 

71 

69.92 

12.33 

69.87 

12.63 

69.81 

12.94 

69.75 

13.24 

7J 

72 

70.91 

12.50 

70.85 

12.81 

70.79 

13.12 

70.74 

13.43 

72 

73 

71.89 

12.68 

71.83 

12.99 

71.78 

13.30 

71.72 

13.62 

73 

74 

72.88 

12.85 

72.82 

13.17 

72.76 

13.43 

72.70 

13.80 

74 

75 

73.86 

13.02 

73.80 

13.35 

73.74 

13.67 

73.68 

13.99 

75 

76 

74.85 

13.20 

74.79 

13.52 

74.73 

13.85 

74.67 

14.18 

76 

77 

75.83 

13.37 

75.77 

13.70 

75.71 

14.0'3 

75.65 

14.36 

77 

78 

76.82 

13.54 

76.76 

13.88 

76.69 

14.21 

76.63 

14.55 

78 

79 

77.80 

13.72 

77.74 

14.06 

77.68 

14.40 

77.61 

14.74 

79 

80 

78.78 

13.89 

78.72 

14.24 

78.68 

14.58 

78.60 

14.92 

80 

81 

79.77 

14.07 

79.71 

14.41 

79.64 

14.76 

79.58 

15.11 

81 

82 

80.75 

14.24 

80.69 

14.59 

80.63 

14.94 

80.50 

15.29 

82 

83 

81.74 

14.41 

81.68 

14,77 

81.01 

15.13 

81 .54 

15.48 

83 

84 

82.72 

14.59 

82.66 

14.95 

82.59 

15.31 

82.53 

15.67 

84 

85 

83.71 

14.76 

83.64 

15.13 

83.58 

15.49 

83.51 

15.85 

85 

86 

84.69 

14.93 

84.63 

15.30 

84.56 

15.67 

84.49 

16.04 

86 

87 

85.68 

15.11 

85.61 

15.48 

85.54 

15.85 

85.47 

16.23 

87 

88 

86.66 

15.28 

86.60 

15.66 

86 .53 

16.04 

86.46 

16.41 

88 

89 

87.65 

15.45 

87.58 

15.84 

87.51 

16.22 

87.44 

16.60 

89 

90 

88.63 

15.63 

88.56 

16.01 

88.49 

16.40 

88.42 

16.79 

90 

91 

89.62 

15.80 

89.55 

16.19 

89.48 

16.53 

89.40 

16.97 

91 

92 

90.60 

15.98 

90.53 

16.37 

90.46 

16.77 

90.39 

17-16 

92 

93 

91.59 

16.15 

91.52 

16.55 

91.44 

10.95 

91.37 

17.35 

93 

94 

92.57 

16.32 

92.50 

16.73 

92.43 

17.13 

92.35 

17.53 

94 

95 

93.56 

16.50 

93.48 

16.90 

93.41 

17.31 

93.33 

17.72 

95 

96 

94.54 

, 16.67 

94.47 

17.08 

94.39 

17.49 

94.32 

17.91 

96 

97 

95.53 

16.84 

95.45 

17.26 

95.38 

17.68 

95.30 

18.09 

97 

98 

96.51 

17.02 

96.44 

17.44 

96.36 

17.86 

96.28 

18.28 

98 

99 

97.50 

17.19 

97.42 

17.62 

97.34 

18.04 

97.26 

18.47 

99 

100 

98.48 

17.36 

98.40 

( 17.79 

98.33 

18.22 

98.25 

18.65 

100 

q5 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

<u 

u 

a 

ci 

•*-> 

w 

c 

80 Deg. 

79! Deg. 

791 

! 

> 

Deg. 

79! Deg. 

•M 

72 

• H 

o 

1 



























































































































24 


TRAVERSE TABLE. 


6 
»— • 

w 

11 Deg. 

lli Deg. 

11 £ 

Deg. 

Ilf Deg. 

O 

in ’ 

c-+- 

P 

3 

o 

re 

■ 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

o 

1 

0.93" 

0.19 

0.98 

0.20 

0.98 

0.20 

0.98 

0.20 

1 

2 

1.96 

0.38 

1.96 

0.39 

1.96 

0.40 

1.96 

0.41 

2 

3 

2.94 

0.57 

2.94 

0.59 

2.94 

0.60 

2.94 

0.61 

3 

4 

3.93 

0.76 

3.92 

0.78 

3.92 

0.80 

3.92 

0.82 

4 

5 

4.91 

0.95 

4.90 

0.98 

4.90 

1.00 

4.90 

1.02 

5 

6 

5.89 

1.14 

5.88 

1.17 

5.88 

1.20 

5.87 

1.22 

6 

7 

6.87 

1.34 

6.87 

1.37 

6.86 

1.40 

6.85 

1.43 

7 

8 

7.85 

1.53 

7.85 

1.56 

7.84 

1.59 

7.83 

1.63 

8 

9 

8.83 

1.72 

8.83 

1.76 

8.82 

1.79 

8.81 

1.83 

9 

10 

9.82 

1.91 

9.81 

1.95 

9.80 

1.99 

9.79 

2.04 

10 

11 

10.80 

2.10 

10.79 

2.15 

10.78 

2.19 

10.77 

2.24 

11 

12 

11.78 

2.29 

11.77 

2.34 

11.76 

2.39 

11.75 

2.44 

12 

13 

12.76 

2.48 

12.75 

2.54 

12.74 

2.59 

12.73 

2.65 

13 

14 

13.74 

2.67 

13.73 

2.73 

13.72 

2.79 

13* 71 

2.85 

14 

15 

14.72 

2.86 

14.71 

2.93 

14.70 

2.99 

14.69 

3.06 

15 

16 

15.71 

3.05 

15.69 

3.12 

15.68 

3.19 

15.66 

3.26 

16 

17 

16.69 

3.24 

16.67 

3.32 

16.66 

3.39 

16.64 

3.46 

17 

18 

17.67 

3.43 

17.65 

3.51 

17.64 

3.59 

17.62 

3.66 

18 

19 

18.65 

3.63 

18.63 

3.71 

18.62 

3.79 | 

18.60 

3.87 

19 

20 

19.63 

3.82 

19.62 

3.90 

19.60 

3.99 

19.58 

4.07 

20 

21 

20.61 

4.01 

20.60 

4.10 

20.58 

4.19 

20.56 

4.28 

21 

22 

21.60 

4.20 

21.58 

4.29 

21.56 

4.39 

21.54 

4.48 

22 

23 

22.58 

4.39 

22.56 

4.49 

22.54 

4.59 | 

22.52 

4.68 

23 

24 

23.56 

4.58 

23.54 

4.68 

23.52 

4.78 j 

23.50 

4.89 

24 

25 

24.54 

4.77 

24.52 

4.88 

24.50 

4.98 j 

24.48 

5.09 

25 

26 

25.52 

4.98 

25.50 

5.07 

25.48 

5.18 l 

25.46 

5.30 

26 

27 

26.50 

5.15 

26.48 

5.27 

26.46 

5.38 

28.43 

5.50 

27 

28 

27.49 

5.34 

27.46 

5.48 

27.44 

5.58 

27.41 

5.70 

28 

29 

28.47 

5.53 

28.44 

5.66 

28.42 

5.78 

28.39 

5.91 

29 

30 

29.45 

5.72 

29.42 

5.85 

29.40 

5.98 

29.37 

6.11 

30 

31 

30.43 

5.92 

30.40 

6.05 

30.38 

6.18 

30.35 

6.31 

31 

32 

31.41 

6.11 

31.39 

6.24 

31.36 

6.33 

31.33 

6.52 

32 

33 

32.39 

6-30 

32.37 

6.44 

32.34 

6.58 

32.31 

6.72 

33 

34 

33.38 

6.49 

33.35 

6.63 

33.32 

6.78 

33.29 

6.92 

34 

35 

34.35 

6.68 

34.33 

6.83 

34.30 

6.93 

34.27 

7.13 

35 

36 

35.34 

6.87 

35.31 

7.02 

35.28 

7.18 ! 

35.25 

7.33 

36 

37 

36.32 

7.06 

36.29 

7.22 

36.26 

7.38 

36.22 

7.53 

37 

38 

37.30 

7.25 

37.27 

7.41 

37.24 

7.58 

37.20 

7.74 

38 

39 

38.28 

7.44 

38.25 

7.61 

38.22 

7.78 

38.18 

7.94 

39 

40 

39.27 

7.63 

39.23 

7.80 

39.20 

7.97 

39.16 

8.15 

40 

41 

40.25 

7.82 

40.21 

8.00 

40.18 

8.17 

40.14 

8.35 

41 

42 

41 23 

8.01 

41.19 

8.19 

41.16 

8.37 

41.12 

8 .55 

42 

43 

42.21 

8.20 

42.17 

8.39 

42.14 

8.57 

42.10 

8.76 

43 

44 

43.19 

8.40 

43.15 

8.58 

43.12 

8 .77 

43.08 

8.96 

44 

45 

44.17 

8.59 

44.14 

8.78 

44.10 

8.97 

44.06 

9.16 

45 

46 

45.15 

8.78 

45.12 

8.97 

45.08 

9.17 

45.04 

9.37 

46 

47 

46.14 

8.97 

46.10 

9.17 

46.06 

9.37 

46.02 

9.57 

47 

48 

47.12 

9.16 

47.08 

9.36 

47.04 

9.57 

46.99 

9.78 

48 

49 

48.10 

9.35 

48.06 

9.50 

48.02 

9.77 

47.97 

9.98 

49 

50 

49.08 

9.54 

49.04 

9,75 

49.00 

9.97 

43.95 

10.18 

50 

« 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

C 

d 

CO 

3 

L_ 

79 Deg. 

i 

7ft} Dog. 


Deg. 

78} Deg. 

£ 

C/2 

| 5 














































































































TRAVERSE TABLE 


25 


»—I 

• 

VI 

r+- 

Pi 

11 

Deg. 

lli Degr. 

U* 

Deg. 

11| Deg. 

i 

C 

r Js * 
pj 

a 

O 

re 

Lat. 

j Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

| Dep. 

a 

o 

re 

51 

50.06 

9.73 

50.02 

9.95 

49.98 

10.17 

49.93 

10.39 

51 

52 

51.04 

9.92 

51.00 

10.14 

50.96 

10.37 

150.91 

10.59 

52 

53 

52.03 

! io.li 

|51.98 

10.34 

51.94 

10.57 

51.89 

10.79 

53 

54 

53.01 

| 10.30 

! 52.96 

10.53 

52.92 

10.77 

52.87 

11.00 

54 

55 

53.99 

10.49 

1 53.94 

10.73 

53.90 

10.97 

53.85 

11.20 

55 

56 

54.97 

:10.69 

54.92 

10.93 

64.8S 

11.16 

54.83 

11.40 

56 

57 

55.95 

10.88 

55.90 

11.12 

55.86 

11.36 

55.Si 

11.61 

57 

53 

56.93 

11.07 

56.89 

11.32 

56.84 

11.56 

56.78 

11.81 

58 

59 

57.92 

11.26 

57.87 

11.51 

57.82 

11.76 

57.76 

12.01 

59 

60 

58.90 

11.45 

58.85 

11.71 

58.80 

11.96 

58.74 

12.22 

60 

61 

59.88 

j 11.64 

59.83 

11.90 

59.78 

12.16 

59.72 

12.42 

61 

62 

60.86 

11.83 

60.81 

12.10 

60.76 

12.33 

60.70 

12.63 

62 

63 

61.84 

12.02 

61.79 

12.29 

61.74 

12.56 

61.68 

12.83 

63 

64 

62.82 

12.21 

62.77 

12.49 

62.72 

12.76 

62.66 

13.03 

64 

65 

63.81 

12.40 

63.75 

12.68 

|63.70 

12.96 

63.64 

13.24 

65 

66 

64.79 

12.59 

64.73 

12.88 

64.68 

13.16 

64.62 

13.44 

66 

67 

65.77 

12.78 

65.71 

13.07 

65.66 

13.36 

65.60 

13.64 

67 

6 S 

66.75 

12.98 

66.69 

13.27 

66.63 

13.56 

66.58 

13.85 

63 

69 

67.73 

13.17 

67.67 

13.46 

67.61 

13.76 

67.55 

14.05 

69 

70 

68.71 

13.36 

68.66 

13.66 

68.59 

13.96 

68.53 

14.25 

70 

71 

69.70 

13.55 

69.64 

13.85 

69.57 

14.16 

69.51 

14.46 

71 

72 

70.68 

13.74 

70.62 

14.05 

70.55 

14.35 

70.49 

14.66 

72 

73 

71.66 

13.93 

71.60 

14.24 

71.53 

J 4.55 

71.47 

14.87 

73 

74 

72.64 

14.12 

72.58 

14.44 

72.51 

14.75 

1 72.45 

15.07 

74 

75 

73.62 

14.31 

73.56 

14.63 

73.49 

14.95 

I 73.43 

15.27 

75 

76 

74.60 

14.50 

74.54 

14.83 

74.47 

15.15 

74.41 

15.48 

76 

77 

75.59 

14.69 

75.52 

15.02 

75.45 

15.35 

75 39 

15.68 

77 

78 

76.57 

14.88 

76.50 

15.22 

76.43 

L5.55 

76.37 

15.88 

78 

79 

77.55 

15.07 

77.48 

15.41 

77.41 

15.75 

77.34 

16.09 

79 

80 

78.53 

15.26 

78.46 

15.61 

78.39 

15.95 

78.32 

16.29 

80 

■ 81 

79.51 

15.46 

79.44 

15.80 

79.37 

16.15 i 

79.30 

16.49 

81 

82 

80.49 

15.65 

80.42 

16.00 

80.35 

16.35 

80.28 

16 *.70 

82 

83 

81.48 

15.84 

81.41 

16.19 

81.33 

16.55 

81.26 

16.90 

83 

84 

82.46 

16.03 

82.39 

16.39 

82.31 

16.75 

82.24 

17.11 

84 

85 

83.44 

16.22 

83.37 

16.58 

83.29 

16.95 

83.22 , 

17.31 

85 

88 

84.42 

16.41 

84.35 

16.78 

84.27 

17.15 

84.20 

17.51 

86 

87 

85.40 

16.60 

85.33 

16.97 

85.25 

17.35 

85.18 | 

17.72 

87 

83 

86.38 

16.79 

86.31 

17.17 

86.23 

17.54 

86.16 

17.92 

88 

89 

87.36 

16.98 

87.29 

17.36 

87.21 

17.74 

87.14 

18.12 

89 

90 

88.35 

17.17 

88.27 

17.56 

88.19 | 

17.94 

88.11 

18.33 

90 

91 

89.33 

17.36 

89.25 

17.75 

89.17 i 

18.14 

89.09 

18.53 

91 

92 

90.31 

17.55 

90.23 

17.95 

90.15 

18.34 

90.07 

18.74 

92 

93 

91.29 

17.75 

91.21 

18.14 j 

91.13 

18.54 

91.05 

18.94 

93 

94 

92.27 

17.94 

92.19 

18.34 

92.11 

18.74 

92.03 

19.14 

94 

95 

93.25 

18.13 

93.17 

18.53 ! 

93.09 

18.94 

93.01 

19.35 

95 

96 

94.24 

18.32 

94.16 

18.73 

94.07 

19.14 1 

93.99 

19.55 

96 

97 

95.22 

18.51 

95.14* 

18.92 

95.05 | 

19.34 

94.97 

19.75 

97 

| 98 

96.20 

18.70 

96.12 

19.12 

96.03 

19.54 

95.95 

19.96 

98 

99 

97.18 

18.89 

97.10 

19.31 

97.01 

19.74 

98.93 

20.16 

99 

100 

98.16 

19.08 

98.08 

19.51 

97.99 | 

19.94 

97.90 

20.36 

100 

<E 

V 

a 

Dcp. 

Lat. 

Dep. | 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

© 

© J 

r-* 1 

c3 

*-> 

00 
• H 

a 

79 Deg. 

78| Deg. 

78A Dog. 

H 

78i Deg. 

cd 5 

5 ’ 

j 











































































































































TRAVERSE TABLE 


26 


o 

ST 

12 Deg 

12} Deg. 

m 

D eg. 

124 Dog. 

*— • 

C/5 

«“► 

2 

rt 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

£3 

O 

p 

i 

0.98 

0.21 

0.98 

0.21 

0.98 

0.22 

0.98 

0.22 

1 

2 

1.96 

0.42 

1.95 

0.42 

1.95 

0.43 

1.95 

0.44 

2 

3 

2.93 

0.62 

2.93 

0.64 

2.93 

0.05 

2.93 

0.66 

3 

4 

3.91 

0.83 

3.91 

0.85 

3.91 

0.87 

3.90 

0.88 

4 

5 

4.89 

1.04 

4.89 

1.06 

4.S8 

1.08 

4.88 

1.10 

5 

6 

5.87 

1.25 

5.86 

1.27 

5.86 

1.30 

5.85 

1.32 

6 

7 

6.85 

1.46 

6.84 

1.49 

6.83 

1.52 

6.S3 

1.54 

7 

8 

7.83 

1.68 

7.82 

1.70 

7.81 

1.73 

7.80 

1.77 

8 

9 

8.80 

1.87 

8.80 

1.91 

8.79 

1.95 

8.78 

1.99 

9 

10 

9.78 

2.08 

9.77 

2.12 

9.76 

2.16 

9.75 

2.21 

10 

11 

10.76 

2.29 

10.75 

2.33 

10.74 

2.38 

10.73 

2.43 

1 1 

12 

11.74 

2.49 

11.73 

2.55 

11.72 

2.60 

11.70 

2.65 

12 

13 

12.72 

2.70 

12.70 

2.76 

12.69 

2.81 

12.68 

2.87 

13 

14 

13.69 

2.91 

13.68 

2.97 

13.67 

3.03 

13.65 

3.09 

14 

15 

14.67 

3.12 

14.66 

3. 18 

14.64 

3.25 

14.63 

3.31 

15 

16 

15.6-5 

3.33 

15.64 

3.39 

15.62 

3.46 

15.61 

3.53 

16 

17 

16.63 

3.53 

16.61 

3.61 

16.60 

3.68 

16.58 

3.75 

17 

18 

17.61 

3.74 

17.59 

3.82 

17.57 

3.90 

17.56 

3.97 

18 

19 

18.58 

3.95 

18.57 

4.03 

18.55 

4.11 

18.53 

4.19 

19 

20 

19.56 

4.16 

19.54 

4.24 

19.53 

4.33 

19.51 

4.41 

20 

21 

20.54 

4.37 

20.52 

4.46 

20.50 

4.55 

20.48 

4.63 

21 

22 

21.52 

4.57 

21.50 

4.67 

21.48 

4.76 

21.46 

4.86 

00 

23 

22.50 

4.78 

22.48 

4.88 

22.45 

4.98 

22.43 

5.03 

23 

24 

23.48 

4.99 

23.45 

5.09 

23.43 

5.19 

23.41 

5.30 

24 

25 

24.45 

5.20 

24.43 

5.30 

24.41 

5.41 

24.33 

5.52 

25 

26 

25.43 

5.41 

25.41 

5.52 

25.38 

5*. 63 

|25.36 

5.74 

26 

27 

26.41 

5.61 

26.39 

5.73 

26.36 

5.84 

26.33 

5.96 

27 

28 

27.39 

5.82 

27.36 

5.94 

27.34 

6.06 

27.31 

6.1S 

28 

29 

28.37 

6.03 

28.34 

6.15 

28.31 

6.28 

23.28 

6.40 

29 

30 

29.34 

6.24 

29.32 

6.37 

29.29 

6.49 

29.26 

6.62 

30 . 

31 

30.32 

6.45 

30.29 

6.58 

30.27 

6.71 

30.24 

6.84 

31 

32 

31.30 

6.65 

31.27 

6.79 

31.24 

6.93 

31.21 

7.06 

32 

33 

32.28 

6.86 

32.25 

7.00 

32.22 

7.14 

32.19 

7.28 

33 

34 

33.26. 

7.07 

33.23 

7.21 

33.19 

7.36 

33.16 

7.50 

34 

35 

34.24 

7.28 

34.20 

7.43 

34.17 

7.58 

34.14 

7.72 

35 

36 

35.21 

7.48 

35.18 

7.64 

35.15 

7.79 

35.11 

7.95 

36 

37 

35.19 

7.69 

36.16 

7.85 

36.12 

8.01 

136.09 

8.17 

37 

38 

37.17 

7.90 

37.13 

8.06 

37.10 

8.22 

!37.06 

8.39 

33 

39 

38.15 

8.11 

38.11 

8.27 

38.08 

8 44 

38.04 

8.61 

39 

40 

39.13 

8.32 

39.09 

8.49 

39.05 

8.66 

|39.01 

8.83 

40 

41 

40.10 

8.52 

40.07 

8.70 

40.03 

8.87 

i39.99 

9.05 

41 

42 

41.08 

8.73 

41.04 

8.91 

41.00 

9.09 

40.96 

9.27 

42 

43 

42.06 

8.94 

4?. 02 

9.12 

41.98 

9.31 

141.94 

9.49 

43 

44 

43.04 

9.15 

43.00 

9.34 

42.96 

9.52 

142.92 

9.71 

44 

45 

44.02 

9.36 

43.98 

9.55 

43.93 

9.74 

!43.89 

9.93 

45 

46 

44.99 

9.56 

44.95 

9.76 

44.91 

9.96 

44.87 

10.15 

46 

47 

45.97 

9.77 

45.93 

9.97 

45.89 

10.17 

45.84 

10.37 

47 

48 

46.95 

9.98 

46.91 

10.18 

46.86 

10.39 

i46.82 

10.59 

43 

49 

47.93 

10.19 

47.88 

10.<10 

47.84 

10.61 

!47.79 

10.81 

49 

50 

48.91 

10.40 

48.86 

10.61 

48.81 

10.82 

j 48.77 

11.03 

50 

o 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 Dep. 

Lat. 

O 

O 

& 

\ ■* 

) a 

78 Deg 

77| Deg. 

771 

Deg. 

1 

77} Deg. 

cd 

+4 

73 

r*N 

































































































TRAVERSE TABLE. 


27 


o 

xn 

<-*■ 

P 

12 Deg. 

12} Deg. 

1 

lOJL 

Deg. 

12} Deg. 

?■ 

r* 

3 

o 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

j Dep. 

Lat. 

Dep. 


5 i 

49.89 

10.60 

49.84 

10.82 

49.79 

11.04 

49.74 

11.20 

51 

52 

50. S6 

10.81 

50.82 

11.03 

|50.77 

11.25 

50.72 

11.48 

52 

53 

51.84 

11.02 

51.79 

11.25 

51.74 

11.47 

51.69 

11.70 

i 53 

54 

52.82 

11.23 

52.77 

11.46 

|52.72 

11.69 

52.67 

11.92 

1 54 

55 

53.80 

11.44 

53.75 

11.67 

53.70 

11.90 

53.64 

12.14 

1 55 

50 

54.78 

11.64 

54.72 

11.88 

54.67 

12.12 

54.62 

12.36 

1 56 

57 

55.75 

11.85 

55.70 

12.09 

155.65 

12.34 

55.59 

12.58 

57 

58 

56.73 

12.06 

56.68 

12.31 

i56.63 

12.55 

56.57 

12.80 

1 58 

59 

57.71 

12.27 

57.66 

12.52 

j57.60 

12.77 

157.55 

13.02 

j 59 

GO 

58.69 

12.47 

58.63 

12.73 

58.58 

12.99 

58.52 

13.24 

! no 

61 

59.67 

12.68 

59.61 

12.94 

59.55 

13.20 

59.50 

13.46 

61 

62 

60.65 

12.89 

60.59 

13.16 

60.53 

13.42 

00.47 

13.68 

62 

03 

61.62 

13.10 

61.57 

13.37 

l61.51 

13.04 

61.45 

13.90 

63 

64 

62.60 

13.31 

62.54 

13.58 

|62.48 

13.85 

62.42 

14.12 

64 

65 

63.58 

13.51 

63.52 

13.79 

:63.46 

14.07 

63.40 

14.35 

65 

66 

64.56 

13.72 

64.50 

14.00 

64.44 

14.29 

64.37 

14.57 

66 

67 

65.54 

13.93 

65.47 

14.22 

65.41 

14.50 

65.35 

14.79 

67 

68 

66.51 

14.14 

66.45 

14.43 

66.39 

14.72 

66.32 

15.01 

68 

69 

67.49 

14.35 

67.43 

14.64 

67.36 

14.93 

67.30 

15.23 

69 

70 

68.47 

14.55 

68.41 

14.85 

58.34 

15.15 

68.27 

15.45 

70 

71 

69.45 

14.76 

69.38 

15.06 

69.32 

15.37 

69.25 

15.67 

71 

72 

70.43 

14.97 

70.36 

15.28 

70.29 

15.58 

70.22 

15.8,9 

72 

73 

71.40 

15.18 

71.34 

15.40 

71.27 

15.80 

71.20 

16.11 

73 

74 

72.38 

15.39 

72.32 

15.70 

72.25 

16.02 

72.18 

16.33 

74 

75 

73.36 

15.59 

73.29 

15.91 

73.22 

16.23 

73.15 

16.55 

75 

76 

74.34 

15.80 

74.27 

16.13 

74.20 

16.45 

74.13 

16.77 

76 

77 

75.32 

16.01 

75.25 

18.34 

75.17 

16.67 

75.10 

16.99 

77 

78 

76.30 

16.22 

76.22 

16.55 

76.15 

16.88 

76.03 

17.21 

78 

79 

77.27 

16.43 

77.20 

16.76 

77.13 

17.10 

77.05 

17.44 

79 

80 

78.25 

16.63 

78.18 

16.97 

78.10 

17.32 

78.03 

17.66 

80 

81 

79.23 

16.84 

79.16 

17.19 

79.08 

17.53 

79.00 

17.88 

81 

82 

80.21 

17.05 

80.13 

17.40 

80.06 

17.75 

79.98 

18.10 

82 

83 

81.19 

17.26 

81.11 

17.61 

81.03 

17.96 

80.95 

18.32 

83 

84 

82.16 

17.46 

82.09 

17.82 

82.01 

18.18 

81.93 

18.54 

84 

85 

83.14 

17.67 

83.06 

18.04 

82.99 

18.40 

82.90 

18.76 

85 

86 

84.12 

17.88 

84.04 

18.25 

83.96 

18.61 

83.83 

18.98 

86 

87 

85.10 

18.09 

85.02 

18.46 

84.94 

18.83 

84.85 

19.20 

87 

88 

86.08 

18.30 

86.00 

18.67 

85.91 

19.05 

85.83 

19.42 

88 

89 

87.06 

18.50 

86.97 

18.88 

86.89 

19.26 

86.81 

19.64 

89 

90 

88.03 

18.71 

87.95 

19.10 

87.87 

19.48 

87.78 

19.86 

90 

91 

89.01 

18.92 

88 .93 

19.31 

88.84 

To .70 

88.76 

20.08 

91 

92 

89.99 

19.13 

89.91 

19.52 

89.82 

19.91 

89.73 

20.30 

92 

93 

90.97 

19.34 

90.88 j 

19.73 

90.80 

20.13 

90.71 

20.52 

93 

94 

91.95 

19.54 

91.86 1 

19.94 

91.77 

20.35 

91.68 

20.75 

94 

95 

92.92 

19.75 

92.84 

20.16 

92.75 

20.56 

92.66 

20.97 

95 

96 

93.90 

19.96 

93.81 

20.37 

93.72 

20.78 

93.63 

21.19 1 

96 

97 

94.88 

20.17 

94.79 

20.58 

94.70 

20.99 

94.61 | 

21.41 1 

97 

98 1 

95.86 

20.38 

95.77 

20.79 

95.68 

21.21 

95.58 

21.63 

98 

99 

96.84 

20.58 

96.75 

21.01 1 

96.65 j 

21.43 

96.56 

21.85 

99 

100 

97.81 | 

20.79 

97.72 

21.22 

97.63 j 

21.64 

97.53 [ 

22.07 

100 

o 

c 1 

Dep. 

Lai. 

Dep. j 

Lat. 

Dep. j 

Lat. 

Dep. | 

Lat. 

cJ 

CJ 

B i 

Li 

78 Deg. 

77} Deg 

77f Deg. 

77} Deg. 

CTi 

Q 


































































































28 


TRAVERSE TARLE 


Distance. 

13 Deg. 

134 Deg. 

13A Deg. 

i 

l3.f Deg. 

C 

cn 

C". 

p 

3 

o 

p 

Lat • 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.97 

0.23 

0.97 

0.23 

0.97 

0.23 

0.97 

0.24 

1 

2 

1.95 

0.45 

1.95 

0.46 

1.95 

0.47 

1.94 

0.48 

2 

3 

2.92 

0.67 

2.92 

0.69 

2.92 

0.70 

2.91 

0.71 

3 

4 

3.90 

0.90 

3.89 

0.92 

3.89 

0.93 

3.89 

0.95 

4 

5 

4.87 

1.12 

4.87 

1.15 

4.86 

1.17 

4.86 

1.19 

5 

6 

5.85 

1.35 

5.84 

1.38 

5.83 

1.40 

5.83 

1.43 

6 

7 

6.82 

1.57 

6.81 

1.60 

6.81 

1.63 

6.80 

1.66 

7 

8 

7.80 

1.80 

7.79 

1.83 

7.78 

1.87 

7.77 

1.90 

8 

9 

8.77 

2.02 

8.76 

2.06 

8.75 

2.10 

8.74 

2.14 

9 

10 

9.74 

2.25 

9.73 

2.29 

9.72 

2.33 

9.71 

2.38 

10 

11 

10.72 

2.47 

10.71 

2.52 

10.70 

2.57 

10.68 

2.61 

11 

12 

11.69 

2.70 

11.68 

2.75 

11.67 

2.80 

11.66 

2.85 

12 

13 

12.67 

2.92 

12.65 

2.98 

12.64 

3.03 

12.63 

3.09 

13 

14 

13.64 

3.15 

13.63 

3.21 

13.61 

3.27 

13.60 

3.33 

14 

15 

14.62 

3.37 

14.60 

3.44 

14.59 

3.50 

14.57 

3.57 

15 

1 G 

15.59 

3.60 

15.57 

3.67 

15.56 

3.74 

15.54 

3.80 

16 

17 

16.57 

3.821 

16.55 

3.90 

16.53 

3.97 

16.51 

4.04 

17 

18 

17.54 

4.05 

17.52 

4.13 

17.50 

4.20 

17.48 

4.28 

18 

19 

18.51 

4.27 

18.49 

4.35 

18.48 

4.44 

18.46 1 

4.52 

19 

20 

19.49 

4.50 

19.47 

4.58 

19.45 

4.67 

19.43 

4.75 

20 

21 

20.46 

4.72 

20.44 

4.81 

20.42 

4.90 

20.40 

4.99 

21 

22 

21.44 

4.95 

21.41 

5.04 

21.39 

5.14 

21.37 

5.23 

22 

23 

22.41 

5.17 

22.39 

5.27 

22.36 

5.37 

22.34 

5.47 

23 

24 

23.38 

5.40 

23.36 

5.50 

23.34 

5.60 

23.31 

5.70 

24 

25 

24.36 

5.62 

24.33 

5.73 

24.31 

5.84 

24.28 

5.94 

25 

26 

25.33 

5.85 

25.31 

5.96 

25.28 

6.07 

25.25 

6.18 

26 

27 

26.31 

6.07 

26.28 

6.19 

26.25 

6.30 

26.23 

6.42 

27 

28 

27.28 

6.30 

27.25 

6.42 

27.23 

6.54 

27.20 

6.66 

28 

29 

28.2G 

6.52 

28.23 

6.65 

28.20 

6.77 

28.17 

6.89 

29 

30 

29.23 

6.75 

29.20 

6.88 

29.17 

7.00 

29.14 

7.13 

30 

31 

30.21 

6.97 

30.17 

7.11 

30.14 

7.24 

30.11 

7.37 

31 

32 

31.18 

7.20 

31.15 

7.33 

31.12 

7.47 

31.08 

7.61 

32 

33 

32.15 

7.42 

32.12 

7.56 

32.09 

7.70 

32.05 

7.84 

33 

34 

33.13 

7.65 

33.09 

7.79 

33.06 

7.94 

33,03 

8.08 

34 

35 

34.10 

7.87 

34.07 

8.02 

34.03 

8.17 

34.00 

8.32 

35 

36 

35.08 

8.10 

35.04 

8.25 

35.01 

8.40 

34.97 

8.56 

36 

37 

36.05 

8.32 

36.02 

8.48 

35.98 

8.64 

35.94 

8.79 

37 

38 

37.03 

8.55 

36.99 

8.71 

36.95 

8.87 

36.91 

9.03 

38 

39 

38.00 

8.77 

37.96 

8.94 

37.92 

9.10 

37.88 

9.27 

39 

40 

38.97 

9.00 

38.94 

9.17 

38.89 

9.34 

38.85 

9.51 

40 

41 

39.95 

9.22 

39.91 

9.40 

39.87 

! 9.57 

39.83 

9.75 

41 

42 

40.92 

9.45 

40.88 

9.63 

40.84 

t 9.80 

40.80 

9.98 

42 

43 

41.90 

9 67 

41.86 

9.86 

41.81 

!10.04 

41.77 

10.22 

43 

44 

42.87 

9.90 

42.83 

19.08 

42.78 

10.27 

42.74 

10.46 

44 

45 

43.85 

10.12 

43.80 

10.31 

43.76 

10-.51 

43.71 

10.70 

45 

46 

44.82 

10.35 

44.78 

10.54 

44.73 

10.74 

44.68 

10.93 

46 

47 

45.80 

10.57 

45.75 

10.77 

45.70 

10.97 

45.65 

11.17 

47 

48 

46.77 

10.80 

46.72 

11.00 

46.67 

i11.21 

46.62 

11.41 

48 

49 

47.74 

11.02 

47.70 

11.23 

47.65 

11.44 

47.60 

11.65 

49 

50 

48.72 

11.25 

48.67 

11.46 

48.62 

11.67 

48.57 

11.88 

50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

1 

77 Deg. 

76f Deg. 

76{ 

Deg. 

764 Deg. 













































































































TRAVERSE TABLE. 


29 


5 

IT. 

13 Deg. 

13$ Deg. 

13*. 

A 

Deg. 

13} Deg. 

o 

►—« 

(—*■ 

p 









g- 

“ 

O 

O 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dcp. 

a 

n 

CD 

51 

49.69 

11.47 

49.64 

11.69 

49.59 

11.91 

49.54 

12.12 

5~I 

52 

50.67 

11.70 

50.62 

11.92 

50.56 

12.14 

50.51 

12.36 

52 

53 

51.64 

11.92 

51.59 

12.15 

51.54 

12.37 

51.48 

12.60 

53 

54 

52.62 

12.15 

52.56 

12.38 

52.51 

12.61 

52.45 

12.84 

54 

55 

53.59 

12.37 

53.54 

12.61 

53.48 

12.84 

53.42 

13.07 

55 

56 

54.56 

12.60 

54.51 

12.84 

54.45 

13.07 

54.40 

13.31 

56 

57 

55.54 

12.82 

55.48 

13.06 

55.43 

13.31 

55.37 

13.55 

j 57 

58 

56.51 

13.05 

56.46 

13.29 

56.40 

13.54 

56.34 

13.79 

58 

59 

57.49 

13.27 

57.43 

13.52 

57.37 

13.77 

57.31 

14.02 

59 

60 

58.46 

13.50 

58.40 

13.75 

58.34 

14.01 

! 58.28 

14.26 

60 

61 

59.44 

13.72 

59.38 

13.98 

59.31 

14.24 

59.25 

14.50 

61 

62 

60.41 

13.95 

60.35 

14.21 

60.29 

14.47 

60.22 

14.74 

62 

63 

61.39 

14.17 

61.32 

14.44 

61.20 

14.71 

61.19 

14.97 

63 

64 

62.36 

14.40 

62.30 

14.67 

62.23 

14.94 

62.17 

15.21 

64 

65 

63.33 

14.62 

63.27 

14.90 

63.20 

15.17 

63.14 

15.45 

65 

66 

64.31 

14.85 

64.24 

15.13 

64.18 

15.41 

64.11 

15.69 

66 

67 

65.28 

15.07 

65.22 

15.36 

65.15 

15.64 

65.08 

15.93 

67 

68 

66.26 

15.30 

66.19 

15.59 

66.12 

15.87 

66.05 

16.16 

68 

69 

67.23 

15.52 

67.16 

15.81 

67.09 

16.11 

67.02 

16.40 

69 

70 

68.21 

15.75 

68.14 

16.04 

68.07 

16.34 

67.99 

16.64 

70 

71 

69.18 

15.97 

69.11 

16.27 

69.04 

16.57 

68.97 

16.88 

71 

72 

70.15 

16.20 

70.08 

16.50 

70.01 

16.81 

69.94 

17.11 

72 

73 

71.13 

16.42. 

71.06 

16.73 

70.98 

17.04 

70.91 

17.35 

73 

74 

72.10 

16.65 

72.03 

16.96 

71.96 

17.28 

71.88 

17.59 

74 

75 

73.08 

16.87 

73.00 

17.19 

72.93 

17.50 

72.85 

17.83 

75 

76 

74.05 

17.10 

73.98 

17.42 

73.90 

17.74 

73.82 

18.06 

76 

77 

75.03 

17.32 

74.95 

17.65 

74.87 

17.98 

74.79 

18.30 

77 

78 

76.00 

17.55 

75.92 

17.88 

75.84 

18.21 

75.76 

18.54 

78 

79 

76.98 

17.77 

76.90 

18.11 

76.82 

18.44 

76.74 

18.78 

79 

80 

77.95 

18.00 

77.S7 

18.34 

77.79 

18.68 

77.71 

19.01 

80 

81 

78.92 

18.22 

78.84 

18.57 

78.76 

18.91 

78.68 

19.25 

81 

82 

79.90 

18.45 

79.82 

18.79 

79.73 

19.14 

79.65 

19.49 

82 

83 

80.87 

18.67 

80.79 

19.02 

80.71 

19.38 

80.62 

19.73 

83 

84 

81.85 

18.90 

81.76 

19.25 

81.68 

19.61 

81.59 

19.97 

84 

85 

82.82 

19.12 

82.74 

19.48 

82.65 

19.84 

82.56 

20.20 

85 

86 

83.80 

19.35 

83.71 

19.71 

83.62 

20.08 

83.54 

20.44 

86 

87 

84.77 

19.57 

84.68 

19.94 

84.60 

20.31 

84.51 

20.68 

87 

88 

85.74 

19.80 

85.66 

20.17 

85.57 

20 • 54 

85.48 

20.92 

88 

89 

86.72 

20.02 

86.63 

20.40 

86.54 

20.78 

86.45 

21.15 

89 

90 

87.69 

20.25 

87.60 

20.63 

87.51 

21.01 

87.42 

21.39 

90 

91 

88.67 

20.47 

88.58 

20.80 

88.49 

21.24 

88.39 

21.63 

91 

92 

89.64 

20.70 

89.55 

21.09 

89.46 

21.48 

89.36 

21.87 

92 

93 

90.62 

20.92 

90.52 

21.32 

90.43 

21.71 

90.33 

22.10 

93 

94 

91.59 

21.15 

91.50 

21.54 

91.40 

21.94 

91.31 

22.34 

94 

95 

92.57 

21.37 

92.47 

21.77 

92.38 

22.18 j 

92.28 

22.58 

95 

96 

93.54 

21.60 

93.44 

22.00 

93.35 

22.41 

93.25 

22.82 

96 

97 

94.51 

21.82 

94.42 

22.23 

94.32 

22.64| 

94.22 

23.06 

97 

98 

95.49 

22.05 

95.39 

22.46 

95.29 

22.83 

95.19 

23.29 

98 

99 

96.46 

22.27 

96.36 

22.69 

96.26 

23.11 

96.16 

23.53 

99 

100 

97.44 

22.50 

97.34 

22.92 

97.24 

23.34 

97.13 

23.77 

100 

6 

o 

C 

Dcp. 

Lat. 

Dcp. 

Lat. | 

Dep. 

Lat. 

Dep. 

Lat. 

ci 

CJ 

7i 

77 Deg. 

j 

76} Deg. 

76-?- Deo- 
- 

76} Deg. 

rt 

■n 

, 

a 


21 























































































30 


TRAVERSE TABLE 


Distance. 

14 Deg. 

14J Deg. 

14| Deg. 

14| Deg. 

Distance. 

Lat. ' 

Dep. 

I Jilt* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.97 

0.21 

0.97 

0.25 

0.97 

0.25 

0.97 

0.25 

1 

2 

1.94 

0.48 

1.94 

0.49 

1.94 

0.50 

1.93 

0.51 

O 

M 

3 

2.91 

0.73 

2.91 

0.74 

2.90 

0.75 

2.90 

0.76 

3 

1 4 

3.88 

0.97 

3.88 

0.98 

3.87 

1.00 

3.87 

1 .02 

4 

! 5 

4.85 

1.21 

4.85 

1 .23 

4.84 

1.25 

4.84 

1.27 

5 

; (5 

5.82 

1.45 

5.82 

1.48 

5.81 

1.50 

5.80 

1.53 

6 

7 

6.79 

1.69 

6.78 

1 72 

6.78 

1.75 

6.77 

1.78 

7 

! 8 

7.76 

1.94 

7.75 

1.97 

7.75 

2.00 

7.74 

2.04 

8 

9 

8.73 

2.18 

8.72 

2.22 

8.71 

2.25 

8.70 

2.29 

9 

10 

9.70 

2.42 

9.69 

2.46 

9.68 

2.50 

9.67 

2.55 

10 

11 

10.67 

2.66 I 

10.66 

2.71 | 

10.65 

2.75 

10.64 

2.80 

11 

12 

11.64 

2.90 

11.63 

2.95 

11.62 

3.00 

11.60 

3.06 

12 

13 

12.61 

3.15 

12.60 

3.20 

12.59 

3.25 

12.57 

3.31 

13 

14 

13.58 

3.39 

13.57 

3.45 

13.55 

3.51 

13.54 

3.56 

14 

15 

14.55 

3.63 

14.54 

3.69 

14.52 

3.76 

14.51 

3.82 

15 

16 

15.52 

3.87 

15.51 

3.94 1 

15.49 

4.01 

15.47 

4.07 

16 

17 

16.50 

4.11 

16.48 

4.18 ■ 

18.46 

4.26 

16.44 

4.33 

17 

18 

17.47 

4.35 

17.45 

4.43 [ 

17.43 

4.51 

17.41 

4.58 

IS 

19 

18.44 

4.60 

18.42 

4.68 1 

18.39 

4.76 

18.37 

4.84 

19 

20 

19.41 

4.84 

19.38 

4.92 

19.36 

5.01 

19.34 

5.09 

20 

21 

20.38 

5.08 

20.35 

5.17 

20.33 

5.26 

20.31 

5.35 

21 

22 

21.35 

5.32 

21.32 

5.42 

21.30 

' 5.51 

21.28 

5.60 

22 

23 

22.32 

5.56 ; 

22.29 

5.68 

22.27 

5.76 

22.24 

5.8G 

23 

2 4 

23.99 

5.81 

123.28 

5.91 

23.24 

6.01 

23.21 

6.11 

24 

25 

24.26 

6.05 

24.23 

6.15 

24.20 

6.26 

24.18 

6.37 

25 

26 

25.23 

6.29 

25.20 

6.40 

25.17 

6.51 

25.14 

6.62 

26 

27 

26.20 

6.53 

26.17 

6.65 

26.14 

6.76 

26.11 

6.37 

27 

28 

27.17 

6.77 

27.14 

6.89 

27.11 

7.01 

27.08 

7.13 

28 

29 

28.14 

7.02 

28.11 

7.14 

28.08 

7.26 

28.04 

7.38 

29 

30 

29.11 

7.26 

29.09 

7.38 

29.04 

7.51 

29.01 

7.64 

30 

31 

30.08 

7.50 

30.05 

7.63 

30.01 

7.76 

29.98 

7.89 

31 

32 

31.05 

7.74 

31.02 

7.88 

30.98 

8.01 

30.95 

8.15 

32 

33 

32.02 

7.98 

31.98 

8.12 

31.95 

8.26 

31.91 

8.40 

33 

34 

32.99 

8.23 

32.95 

8.37 

32.92 

8.51 

32.88 

8.60 

34 

35 

33.96 

8.47 

33.92 

8.62 

33.89 

8.78 

33.85 

8.91 

35 

36 

34.93 

8.71 

34.89 

8.86 

34.85 

9.01 

34.81 

9.17 

36 

37 

35.90 

8.95 

35.86 

9.11 

35.82 

9.26 

35.78 

9.42 

37 

38 

36.87 

9.19 

36.83 

9.35 

36.79 

9.51 

36.75 

9.67 

33 

39 

37.84 

9.44 

37.80 

9.60 

37.76 

9.76 

37.71 

9.93 

39 

40 

38.81 

9.68 

33.77 

9.85 

38.73 

10.02 

33.68 

10.18 

40 

41 

39.78 

9.92 

39.74 

10.09 

39.69 

10.27 

39.65 

10.44 

41 

42 

40.75 

10.16 

40.71 

10.34 

40.66 

10.52 

40.62 

10.69 

42 

43 

41.72 

110.40 

41.68 

10.58 

41.63 

10.77 

41.58 

10.95 

43 

44 

42.69 

|10.64 

42.65 

10.83 

42.60 

11.02 

42.55 

11 .20 

44 

45 

43.66 

10.89 

43.62 

11.08 

43.57 

11.27 

43.52 

11.46 

45 

46 

44.63 

11.13 

44.58 

11.32 

44.53 

11.52 

44.48 

11.71 

46 

47 

45.60 

11.37 

45.55 

11.57 

45.50 

11.77 

45.45 

11.97 

47 

48 

46.57 

11.61 

46.52 

11.82 

46.47 

12.02 

46.42 

12.22 

43 

49 

147.54 

11.85 

47.49 

12.08 

47.44 

12.27 

47.39 

12.48 

49 

50 

[48.51 

12.10 

48.46 

12.31 

48.41 

12.52 

48.35 

12.73 

50 

C 

| Distance.’ 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lcit. 

Dep. 

1 Lat. 

Distance. 

76 Deg. 

75| Deg. 

751 Deg. 

15 \ Deg. 


















































































































TRAVERSE TABLE 


. 3 ] 


a 

• 

to 

r+ 

P 

14 Deg. 

14} Deg. 

14J 

Deg. 

14| Deg. 

O 

v:' 

t—+ 

P 

3 

O 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

ra 

51 

49.49 

12.34 

49.43 

12.55 

49.38 

12.77 

49.32 

12.98 

51 

52 

50.46 

12.58 

50.40 

12.SO 

50.34 

13.02 

50.29 

13.24 

52 

53 

51.43 

12.82 

51.37 

13.05 

51.31 

13.27 

51.25 

13.49 

53 

54 

52.40 

13.06 

52.34 

13.29 

52.28 

13.52 

52.22 

13.75 

54 

55 

53.37 

13.31 

53.31 

13.54 

53.25 

13.77 

53.19 

14.00 

n. f 

56 

54.34 

13.55 

54.28 

13.78 

54.22 

14.02 

54.15 

14.26 

56 

5? 

55.31 

13.79 

55.25 

14.03 

55. 18 

14.27 

55. 12 

14.51 

57 

5S 

56.28 

14.03 

56.22 

14.28 

56.15 

14.52 

56.09 

14.77 

58 

59 

57.25 

14.27 

57.18 

14.52 

57. 12 

14.77 

57.06 

15.02 

59 

60, 

58.22 

14.52 

58.15 

14.77 

58.09 

15.02 

58.02 

15.28 

60 

61 

59.19 

14.76 

59.12 

15.02 

59.06 

15.27 

58.99 

15.53 

6! 

62 

60.16 

15.00 

60.09 

15.26 

60.03 

15.52 

59.96 

15.79 

62 

63 

61. 13 

15.24 

61.06 

15.51 

60.99 

15.77 

60.92 

16.04 

63 

64 

62.10 

15.48 

62.03 

15.75 

61.96 

16.02 

i 61.89 

1 6.29 

64 

65 

63.07 

15.72 

63.00 

16.00 

62.93 

16.27 

62.86 

16.55 

65 

66 

64.04 

15.97 

63.97 

16.25 

163.90 

16.53 

63.83 

16.80 

66 

67 

65.01 

16.21 

64.94 

16.49 

|64.87 

16.78 

64.79 

17.06 

67 

68 

65.98 

16.45 

65.91 

16.74 

65.83 

17.03 

65.76 

17.31 

68 

69 

66.95 

16.69 

66.88 

16.98 

66.80 

17.28 

66.73 

17.57 

69 

70 

67.92 

16.93 

67.85 

17.23 

67.77 

17.53 

67.69 

17.82 

70 

71 

68.89 

17. 18 

68.82 

17.48 

68.74 

17.78 

68.66 

18.08 

71 

72 

69.86 

17.42 

69.78 

17.72 

69.71 

18.03 

69.63 

18.33 

72 

73 

70.83 

17.66 

70.75 

17.97 

70.67 

18.28 

70.59 

18.59 

73 

74 

71.80 

17.90 

71.72 

18.22 

71 .64 

18.53 1 

71 .56 

18.84 

74 

75 

72 77 

18.14 

72.69 

18.46 

72.61 

18.78 

72.53 

19.10 

75 

76 

73 74 

18.39 

73.66 

18.71 

73.58 

19.03 ; 

73.50 

19.35 

76 

77 

74.71 

18.63 

74.63 

18.95 

74.55 

19.28 

74.46 

19.60 

77 

78 

75.68 

18.87 

7-L60 

19.20 

75.52 

19.53 

75.43 

1 9.86 

78 

79 

76.65 

19.11 

76.57 

19.45 

76.48 

19.78 

76.40 

20.1 1 

79 

80 

77.62 

19.35 

77.54 

19.69 

77.45 

20.03 

77.36 

20.37 

80 

81 

78.59 

19.60 

78.51 

19.94 

78.42 

20.28 

78.33 

20.62 

81 

82 

79.56 

19.84 

79.48 

20.18 

79.39 

20.53 

79.30 

20.88 

82 

83 

80.53 

20.08 

80.45 

20.43 

SO. 36 

20.78 

80.26 

21.13 

83 

84 

8 1.50 

20.32 

81 .42 

20.68 

81.32 

21.03 

81 .23 

2 1.39 

84 

85 

82.48 

20.56 

82.38 

20.92! 

82.29 

21.28 

82.20 

21 .64 

85 

86 

83.45 

20.81 

83.35 

21.17 

83.26 

21 . 53 : 

83. 17 

21.90 

86 

87 

84.42 

21.05 

84.32 

21.42 

84.23 

21.78 

84.13 

22. 15 

87 

88 

85.39 

21.29 

85.29 

21.66 

85.20 

22.03 

85. 10 

22.41 

88 

89 

86.36 

21.53 

86.26 

21.91 

86. 17 

22.28 

86.07 

22.66 

89 

90 

87.33 

21.77 

87.23 

22.15 

87.13 

22.53 

87.03 

22.91 

90 

91 

88.30 

22.01 

88.20 

22.40 

88.10 

22.78 

88.00 

23.17 

91 

92 

89.27 

22.26 

89.17 

22.65 

89.07 

23.04 

88.97 

23.42 

<»2 

93 

90.24 

22.50 

90.14 

22.89 

90.04 

23.29 

89.94 

23.68 

93 

94 

91.21 

22.74 

91.11 

23.14 

91 .01 

23.54 

90.90 

23.93 

94 

95 

92.18 

22.98 

92.08 

23.38 

91.97 

23.79 

91.87 

24.19 

95 

96 

93.15 

23.22 

93.05 

23 ‘63 

92.94 

24.04 

92.84 

24 .44 

96 

97 

94.12 

23.47 

94.02 

23.88 

93.91 

24.29 

93.80 

24.70 

97 

98 

95.09 

23.71 

94.98 

24.12 

94.88 

24.54 

94.77 

24.95 

98 

99 

96.06 

23 95 

95.95 

24.37 

95.85 

24.79 

95.74 

25.21 

99 

100 

97.03 

24.19 

96.92 

24.62 

96.81 

25.04 

96.70 

25.46 

100 

cJ r 

a 

£ 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

c 

IM 

£ 

*-> 

cn 

S 

70 Deg. 

75| Dog 

nrl 
l i) 2 

Deg. 

75} Deg 

cd 1 

•jj 

3 




































































































32 


TRAVERSE TABLE. 


g 1 

cn 

p**- 

15 Deg. 

15$ Deg. 

15£ 

Deg. 

15.? Deg. 

O 

pT 

3 

o 

? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

D 

O 

1 

0.97 

0.26 

0.96 

0.26 

0.96 

0.27 

0.96 

0.27 

l 

o 

1.93 

0.52 

1.93 

0.53 

1.93 

0.53 

1.92 

0.54 

2 

3 l 

2.90 

0.78 

2.89 

0.79 

2.89 

0.80 

2.89 

0.81 

3 

4 | 

3.86 

1.04 

3.86 

1.05 

3.85 

1.07 

3.85 

1.09 

4 

5 ! 

4.83 

1.29 

4.82 

1.32 

4.82 

1.34 

4.81 

1.36 

5 

6 | 

5.80 

1.55 

5.79 

1.58 

5.78 

1.60 

5.77 

1.63 

6 

7 | 

G .76 

1.81 

6.75 

1.84 

6.75 

1.87 

6.74 

1.90 

7 

8 | 

7.73 

2.07 

7.72 

2.10 

7.71 

2.14 

7.70 

2.17 

8 

9 

8.69 

2.33 

8.63 

2.37 

8.67 

2.41 

8.66 

2.44 

9 

10 

9.66 

2.59 

9.65 

2.63 

9.64 

2.67 

9.62 

2.71 < 

10 

11 

10.63 

2.85 

10.61 

2.89 

10.60 

2.94 

10.59 

2.99 

11 

12 

11.59 

3.11 

11.58 

3.16 

11.56 

3.21 

11.55 

3.26 

12 

13 

12.56 

3.36 

12.54 

3.42 

12.53 

3.47 

12.51 

3.53 

13 

14 

13.52 

3.62 

13.51 

3.68 

13.49 

3.74 

13.47 

3.80 

14 

15 

14.49 

3.83 

14.47 

3.95 

14.45 

4.01 

14.44 

4.07 

15 

16 

15.45 

4.14 

15.44 

4.21 

15.42 

4.28 

15.40 

4.34 

16 

17 

16.42 

4.40 

16.40 

4.47 

16.38 

4.54 

18.36 

4.61 

17 

IS 

17.39 

4.66 

17.37 

4.73 

17.35 

4.SI 

17.32 

4.89 

18 

19 

18.35 

4.92 

18.33 

5.00 

18.31 

5.03 

13.29 

5.16 

19 

20 

19.32 

5.18 

19.30 

5.26 

19.27 

5.34 

19.25 

5.43 

20 

21 

20.28 

5.44 

20.26 

5.52 

20.24 

5.61 

20.21 

5.70 

21 

22 

21.25 

5.69 1 

21.23 

5.79 

21.20 

5.88 I 

21.17 

5.97 

22 

23 

22.22 

5.95 

22.19 

6.05 

22.16 

6.15 1 

22.14 

6.24 

23 

24 

23. 18 

6.21 

23.15 

6.31 

23.13 

6.41 j 

23.10 

6.51 

24 

25 

24.15 

6.47 

24.12 

6.53 

24.09 

6.63 ! 

24.06 

6.79 

25 

26 

25.11 

6.73 

25.08 

6.84 

25.05 

6.95 

25.02 

7.06 

28 

27 

26.08 

6.99 

26.05 

7.10 

26.02 

7.22 

25.99 

7.33 

27 

28 

27.05 

7.25 

27.01 

7.36 

26.93 

7.4S 

20.95 

7.60 

28 

29 

28.01 

7.51 

27.98 

7.63 

27.95 

7.75 

27.91 

7.87 

29 

30 

28.98 

7.76 

28.94 

7.89 

28.91 

8.02 | 

2S.87 

8.14 

30 

31 

29.94 

8.02 

29.91 

8.15 

29.87 

8.28 

29.84 

8.41 

31 

32 

30.91 

8.28 

30.87 

8.42 

30.84 

8.55 

30.80 

8.69 

32 

33 

31.88 

8.54 

31.84 

8.68 

31.80 

8.82 

31.76 

3.96 

33 

34 

32.84 

8.80 

32.80 

8.94 

32.76 

9.09 

32.72 

9.23 

34 

j 35 

33.81 

9.06 

33.77 

9.21 

33.73 

9.35 

33.69 

9.50 

35 

< 36 

34.77 

9.32 

34.73 

9.47 

34.69 

9.62 

34.65 

9.77 

36 

37 

35.74 

9.58 

35.70 

9.73 

35.65 

9.89 

35.61 

10.04 

37 

38 

36.71 

9.84 

36.66 

10.00 

36.62 

10.16 

36.57 

10.31 

38 

39 

37.67 

10.09 

37.63 

10.26 

37.58 

10.42 

37.54 

10.59 

39 

40 

38.64 

10.35 

38.59 

10.52 

38.55 

10.69 

33.50 

10.86 

40 

41 

39.60 

10.61 

39.56 

10.78 

39.51 

10.96 

39.46 

| 11.13 

41 

42 

40.57 

10.87 

40.52 

11.05 

40.47 

11.22 

40.42 

11.40 

42 

43 

41.53 

11.13 

41.49 

11.31 

41.44 

11.49 

41.39 

11.67 

43 

44 

42.50 

11.39 

42.45 

11.57 

42.40 

11.76 

42.35 

11.94 

44 

45 

43.47 

11.65 

43.42 

11.84 

43.36 

12.03 

43.31 

j 12.21 

45 

46 

44.43 

11.91 

| 44.38 

12.10 

44.33 

12.29 

j44.27 

12.49 

46 

47 

45.40 

12.16 

I 45.35 

12.36 

45.29 

12.56 

45.24 

12.76 

47 

48 

46.36 

12.42 

46.31 

12.63 

46.25 

12.83 

, 46.20 

13.03 

48 

49 

47.33 

12.68 

! 47-27 

12.89 

47.22 

13.09 

47.16 

13.30 

49 

50 

48.30 

12.94 

I 48.24 

13.15 

48.18 

13.36 

43.12 

|13.57 

50 

® 

o 

c 

Dep. 

Lat. 

jj De P- 

Lat 

Dep. 

Lat. 

Dep. 

| Lat. 

6 

O 

e 

d 

£ 

ID 

Deg. 

il 

|| "41 Deg. 

74*- 

Deg. 

74? 

Deg. 

ci 

+-> 

Cfj 





























































































































TRAVERSE TABLE. 


33 


o 

5* 

P 

15 Deg. 

15* Deg. 

15i 

Deg. 

15* Deg. 

►—<. 

cn 

3 

o 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat* 

Dep. 

P 

a * 

pt 

51 

49.26 

13.20 

49.20 

13.41 

49.15 

13.63 

49.09 

13.84 

51 

52 

50.23 

13.46 

50.17 

13.68 

50.11 

13.90 

50.05 

14.11 

52 

53 

51.19 

13.72 

51.13 

13.94 

51.07 

14.16 

51.01 

14.39 

53 

54 

52.16 

13.98 

52.10 

14.20 

52.04 

14.43 

51.97 

14.60 

54 

55 

53.13 

14.24 

153.06 

14.47 

53.00 

14.70 

52.91 

14.93 

55 

56 

54.09 

14.49 

54.03 

14.73 

53.96 

14.97 

53.90 

15.20 

56 

57 

55.06 

14.75 

54.99 

14.99 

54.93 

15.23 

54.86 

15.47 

57 

58 

56.02 

15.01 

55.96 

15.26 

55.89 

15.50 

55.82 

15.74 

58 

59 

56.99 

15.27 

56.92 

15.52 

56.85 

15.77 

56.78 

16.01 

59 

60 

57.96 

15.53 

57.89 

15.78 

57.82 

16.03 

57.75 

16.29 

GO 

61 

58.92 

15.79 

58.85 

16.04 

58.78 

16.30 

58.71 

16.56 

61 

62 

59.89 

16.05 

59.82 

16.31 

59.75 

16.57 

59.67 

16.83 

62 

63 

60.85 

16.31 

60.78 

16.57 

60.71 

16.84 

60.63 

17.10 

63 

64 

61.82 

16.56 

61.75 

16.83 

61.67 

17.10 

61.60 

17.37 

64 

65 

62.79 

16.82 

62.71 

17.10 

62.64 

17.37 

62.56 

17.64 

65 

66 

63.75 

17.08 

63.68 

17.35 

63.60 

17.64 

03.52 

17.92 

66 

67 

64.72 

17.34 

64.64 

17.62 

64.56 

17.90 

64.48 

18.19 

67 

68 

65.68 

17.60 

65.61 

17.89 

65.53 

18.17 

65.45 

38.46 

68 

69 

66.65 

17.86 

66.57 

18.15 

66.49 

18.44 

66.41 

3 8.73 

69 

70 

67.61 

18.12 

67.54 

18.41 

67.45 

18.71 

67.37 

19.00 

70 

71 

68.58 

18.38 

68.50 

18.68 

68.42 

18.97 

68.33 

19.27 

71 

72 

69.55 

18.63 

09.46 

18.94 

69.38 

19.24 

69.30 

19.54 

72 

73 

70.51 

18.89 

70.43 

19.20 

70.35 

19.51 

70.26 

19.82 

73 

74 

71.48 

19.15 

71.39 

19.46 

71.31 

19.78 

71.22 

20.09 

74 

75 

72.44 

19.41 

72.36 

19.73 

72.27 

20.04 

72.18 

20.36 

75 

76 

73.41 

19.67 

73.32 

19.99 

73.24 

20.31 

73.15 

20.63 

76 

77 

74.38 

19.93 

74.29 

20.25 

74.20 

20.58 

74.11 

20.90 

77 

78 

75.34 

20.19 

75.25 

20.52 

75.16 

20.84 

75.07 

21.17 

78 

79 

70.31 

20.45 

76.22 

20.78 

76.13 

21.11 

1 76.03 

21.44 

79 

80 

77.27 

20.71 

77.18 

21.04 

77.09 

21 .38 

77.00 

21.72 

80 

81 

78.24 

20.96 

78.15 

21.31 

78.05 

21.65 

77.96 

21.99 

81 

82 

79.21 

21.22 

79.11 

21.57 

79.02 

21.91 

78.92 

22.26 

82 

83 

80.17 

21.48 

80.08 

21.83 

79.98 

22.18 

79.88 

22.53 

83 

84 

81.14 

21.74 

81.04 

22.09 

80.94 

22.45 

80.85 

22.80 

84 

85 

82.10 

22.00 

82.01 

22.36 

SJ .91 

22.72 

81.81 

23.07 

85 

86 

83.07 

22.26 

82.97 

22.62 

82.87 

22.98 

82.77 

23.34 

86 

87 

84.04 

22.52 

83.94 

22.88 

83.84 

23.25 

83.73 

23.62 

87 

88 

85.00 

22.78 

84.90 

23.15 

84.80 

23.52 

84.70 

23.89 

88 

89 

85.97 

23.03 

85.87 

23.41 

85.76 

23.78 

85.66 

24.16 

89 

90 

86.93 

23.29 

86.83 

23.67 

86.73 

24.05 

86.62 

24.43 

90 

91 

87.90 

23.55 

87.80 

23.94 

87.69 

24.32 

87.58 

24.70 

91 

92 

88.87 

23.81 

88.76 

24.20 

88.65 

24.59 

88.55 

24.97 

92 

93 

89.83 

24.07 

89.73 

24.46 

89.62 

24.85 

89.51 

25.24 

93 

94 

90.80 

24.33 

90.69 

24.72 

90.58 

25.12 

90.47 

25.52 

94 

95 

91.76 

24.59 

91.65 

24.99 

91.54 

25.39 

91.43 

25.79 

95 

96 

92 73 

24.85 

92.62 

25.25 

92.51 

25.65 

92.40 

20.06 

96 

97 

93.69 

25.11 

93.58 

25.51 

93.47 

25.92 

93.36 

26.33 

97 

98 

91.66 

25.36 

94.55 

25.78 

94.44 

26.19 

91.32 

26.60 

98 

99 

95.63 

25.62 

95.51 

26.04 

95.40 

26.46 

95.28 

26.87 

99 

100 

96.59 

25.88 

36.48 

26.30 

96.36 

26.72 

96.25 

27.14 

100 

6 

o 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

d 

cn 

75 Deg. 

74| Deg. 

741 

Deg. 

( 

| 74* Deg. 










































































































34 


TRAVERSE TABLE 


Distance. 

• 

16 Deg. 

16| Deg. 

16* Deg. 

16! Deg. 

O 

c r. 

r-»- 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

o 

1 

0.96 

0.28 

0.96 

0.28 

0.96 

0 28 

0.96 

0.29 

1 

2 

1 92 

0.55 

1.92 

0.56 

1.92 

6.57 

1.92 

0.58 

2 

3 

2.88 

0.83 

2.83 

0.84 

2.88 

0.85 

2.87 

0.86 

3 . 

4 

3.85 

1.10 

3.84 

1.12 

3.84 

1.14 

3.83 

1.15 

4 

5 

4.81 

1 .38 

4.80 

1.40 

4.79 

1.42 

4.79 

1.44 

5 

6 

5.77 

1.65 

5.76 

1.68 

5.75 

1.70 

5.75 

1.73 

6 

7 

G. 73 

1.93 

G. 72 

1.96 

6.71 

1 .99 

0.70 

2.02 

7 

8 

7.69 

2.21 

7.68 

2.24 

7.67 

2.27 

7.66 

2.31 

8 

9 

8.65 

2.48 

8.64 

2.52 

8.63 

2.56 

8.62 

2.59 

9 

10 

9.01 

2.76 I 

9.60 

2.80 

9.59 

2.84 

9.58 

2.S8 

10 

1 1 

10.57 

3.03 1 

10.56 

3.08 

10.55 

3.12 

10.53 

3.17 

11 

1 O 

i -v 

11.54 

3.31 ! 

11.52 

3.36 

11.51 

3.41 

11.49 

3.46 

12 

13 

12.50 

3.58 

12.48 

3.64 

12.46 

3.69 

12.45 

3.75 

13 

14 

13.46 

3.86 

13.44 

3.92 

13.42 

3.98 

13.41 

4.03 

14 

15 

14.42 

4.13 

14.40 

4.20 

14.38 

4.26 

14.36 

4.32 

15 

16 

15.33 

4.41 

15.36 

4.48 

15.34 

4.54 

15.32 

4.61 

16 

17 

16.34 

4.69 | 

16.32 

4.76 

16.30 

4.83 

16.28 

4.90 

17 

18 

17.30 

4.96 1 

17.28 

5.04 

17.26 

5.11 

17.24 

5.19 

18 

19 

18.26 

5.24 i 

18.24 

5.32 

18.22 

5.40 

18.19 

5.48 

19 

20 

19.23 

5.51 

19.20 

5.60 

19.18 

5.68 

19.15 

5.76 

20 

21 

20.19 

5.79 

20 . 16 

5.88 

20.14 

5.96 

20.11 

6.05 

21 

22 

21.15 

6.06 1 

21.12 

6.16 

21.09 

6.25 

21.07 

6.34 

22 

23 

22 . 1 1 

6.34 i 

22.08 

6.44 

22.05 

6.53 

22.02 

6 .63 

23 

24 

23.07 

6.62 

23.04 

6.72 

23.01 

6.82 1 

22.98 

6.92 

24 

25 

24.03 

6.89 

24.00 

7.00 

23.97 

7. 10 

23.94 

7.20 

25 

26 

24.99 

7.17 

24.96 

7.28 

24.93 

7.33 

24.90 

7.49 

26 

27 

25.95 

7.44 

25.92 

7.56 

25.89 

7.67 

25.85 

7.78 

27 

28 

26.92 

7.72 

26.88 

7.84 

26.85 

7.95 

26.81 

8.07 

28 

29 

27.83 

7.99 

27.S4 

8.111 

27.81 

8.24 

27.77 

8.36 

29 

30 

23.84 

8.27 

28.80 

8.39 

28.76 

8.52 

28.73 

8.65 

30 

31 

29.80 

8 .54 

29.76 

8.67 

29.72 

8.80 

29.68 

8.93 

31 

32 

30.76 

8.82 

30.72 

8.95 

30.68 

9.09 

30.64 

9.22 

32 

33 

31.72 

9.10 

31.68 

9.23 

31.64 

9.37 

31.60 

9.51 

33 

34 

32.68 

9.37 

32.64 

9.51 

32.60 

9.66 

32.56 

9.80 

34 

35 

33.64 

9.65 

33.60 

9.79 

33.56 

9.94 

33.51 

10.09 

35 

36 

34.61 

9.92 

34.56 

10.07 

34.52 

10.22 

34.47 

10 .3S 

36 

37 

35.57 

10.20 

35.52 

10.35 

35.48 

10.51 

35.43 

10.66 

37 

3S 

36.53 

10.47 

35.48 

10.63 

36.44 

10.79 

36.39 

10.95 

38 

39 

37.49 

10.75 

37-44 

10.91 

37.39 

11 . 03 

37.35 

11.24 

39 

40 

38.45 

11.03 

38.40 

11.19 

38.35 

11 .36 

38.30 

11.53 

40 

41 

39.41 

11.30 

1 39.36 

11.47 

39.31 

11.64 

39.26 

11.82 

41 

42 

40.37 

11.58 

40.32 

11.75 

40.27 

11.93 

40.22 

12.10 

42 

43 

41.33 

11.85 

41.28 

12.03 

41.23 

12.21 

41.18 

12.39 

43 

44 

42.30 

12.13 

42.24 

12.31 

42. 19 

12.50 

42.13 

12.68 

44 

45 

43.26 

12.40 

43.20 

12.59 

43.15 

12.73 

43.09 

12.97 

45 

46 

44.22 

12.68 

44.16 

12.87 

44.11 

13.06 

44.05 

13.26 

46 

47 

45.18 

12.95 

45.12 

13.15 

45.0G 

13.35 

45.01 

13.55 

47 

48 

46.14 

13.23 

46.08 

13.43 

46.02 

13.63 

45.96 

13.83 

48 

49 

47.10 

13.51 

47.04 

13.71 

46.98 

13.92 

46.92 

14.12 

49 

50 

48.06 

13.78 

48.00 

13.99 

47.94 

14.20 

47.88 

14.41 

50 

• 

o 

CJ 

*—* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

c 

w 
. —* 

Cl 

74 Deg. 

73| Deg. 

731 

Deg. 

73! Deg. 

ri 

Tr 

£ 

* 1 


I 














































































































TR A.V ERS E TABLE. 


35 


Distance.j 

16 Deg. 

16^ Deg. 

16;V 

- 

1 

Deg 

1 

16| Deg. 

Distance. 

Lat. 

Dcp. 

Lat. | 

I 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

49 02 

14.06 

48.96 

14.27 

48.90 

14.48 

48.84 

14.70 

51 

52 

49.99 

14.33 

49.92 

14.55 

49.86 

14.77 

49.79 

14.99 

52 

53 

50.95 

14.61 

50.88 

14.83 

50.82 

15.05 

50.75 

15.27 

53 

54 

51.91 

14.88 

51.84 

15.11 

51.78 

15.34 

51.71 

15.56 

54 

55 

52.87 1 

15.16 

52.80 

15.39 

52.74 

15.62 

52.67 

15.85 

55 

50 

53. S3 

15.44 

53.76 

15.67' 

53.69 

15.90 

53.62 

16.14 

56 

57 

54.79 

15.71 

54.72 

15.95 

54.65 

16.19 

54.58 

16.43 

57 

58 

55.75 

15.99 

55.68 

16.23 

55.61 

16.47 1 

55.54 

16.72 

58 

59 

50.71 

16.26 

56.64 

16.51 

56.57 

16.76 

56.50 

17.00 

59 

00 

57.68 

16.54 

57.60 

16.79 

57.53 

17.04 

5 l • 4:0 

17.29 

60 

01 

58.64 

16.81 

58.56 

17.07 

58.49 

17.32 

58.41 

17.58 

61 

62 

59.60 

17.09 

59.52 

17.35 

59.45 

17.61 

59.37 

17.87 

62 

63 

60.56 

17.37 

60.48 

17.63 

60.41 

17.89 

60.33 

18.16 

63 

04 

61.52 

17.04 

61.44 

17.91 

61.36 

18.18 

61.28 

18.44 

64 

05 

02.48 

17.92 

62.40 

18.19 

62.32 

18.46 

62.24 

18.73 

65 

GO 

03.44 

18.19 ! 

63.36 

18.47 

63.28 

18.74 

63.20 

19.02 

66 

67 

64.40 

18.47 ' 

64.32 

18.75 

64.24 

19.03 

64.16 

19.31 

67 

68 

65.37 

18.74 

65.28 

19.03 

65.20 

19.31 

65.11 

19.60 

68 

69 

60.33 

19.02 

66.24 

19.31 

66.16 

19.60 

66.07 

19.89 

69 

70 

67.29 

19.29 

67.20 

19.59 

67.12 

19.88 

67.03 

20.17 

70 

71 

68.25 

19.57 

68 . 16 

19.87 

68.08 

20.17 

07.99 

20.46 

71 

72 

69.21 

19.85 

69. 12 

20.15 

69.03 

20.45 

68.95 

20.75 

72 

73 

70.17 

20.12 

70.08 

20.43 

69.99 

20.73 

69.90 

21.04 

73 

74 

71.13 

20.40 

71.04 

20.71 

70.95 

21.02 

70.86 

21.33 

74 

75 

72.09 

20.67 

72.00 

20.99 

71.91 

21.30 

71.82 

21 .61 

75 

76 

73.06 

20.55 

72.96 

21.27 

72.87 

21.59 

,72.78 

21.90 

76 

77 

74.02 

21.22 

73.92 

21.55 

73.83 

21.87 

73.73 

22.19 

77 

78 

74.98 

21.50 

74.88 

21 .83 

74.79 

22.15 

74.69 

22.48 

78 

79 

75.94 

21.78 

75.84 

22.11 

75.75 

22.44 

75.65 

22.77 

79 

80 

76.90 

22.05 

76.80 

22.39 

76.71 

22.72 

| 76.61 

23.06 

80 

81 

77.80 

22.33 

77.76 

22.67 

77.66 

23.01 

I 77.56 

23.34 

'81 

82 

78.82 

22.60 

78.72 

22.95 

78.62 

23.29 

i 78.52 

23.63 

82 

83 

79.78 

22.88 

79.68 

23.23 

79.58 

23.57 

| 79.48 

23.92 

83 

84 

80.75 

23.15 

80.64 

23.51 

80.54 

23.86 

80.44 

24.21 

84 

85 

81.71 

23.43 

81.60 

23.79 

81.50 

24.14 

81 .39 

24.50 

85 

80 

82.67 

23.70 

82.56 

24.07 

82.46 

24.43 

1 82.35 

24.78 

86 

87 

83.63 

23.98 

83.52 

24.35 

83.42 

24.71 

83.31 

25.07 

87 

88 

84.59 

24.20 

84.48 

24.62 

84.38 

24.99 

84.27 

25.36 

88 

89 

85.55 

24.53 

85.44 

24.90 

85.33 

25.28 

85.22 

25.65 

89 

90 

80.51 

24.81 

86.40 

25.18 

86.29 

25.56 

86.18 

25.94 

90 

91 

87.47 

25.08 

8 7.36 

25.46 

87.25 

25.85 

87.14 

26.23 

91 

92 

88.44 

25. .36 

88.32 

25.74 

88.21 

26.13 

88.10 

26.51 

92 

93 

89.40 

25.63 

89.28 

26.02 

S9.17 

26.41 

89.05 

26.80 

93 

94 

90.36 

25.91 

90.24 

26.30 

90.13 

26.70 

90.01 

27.09 

94 

95 

91.32 

26.19 

91.20 

26.58 

91.09 

26.98 

90.97 

27.38 

95 

96 

32.28 

26.46 

92.16 

26.86 

92.05 

27.27 

!91.93 

27.67 

96 

97 

93.24 

26.74 

93.12 

27.14 

93.01 

27.55 

92.88 

27.95 

97 

98 

94.20 

27.01 

94.08 

27.42 

93.96 

27.83 

93.84 

28.24 

98 

99 

95.16 

27.29 

95.04 

27.70 

94.92 

28.12 

94.80 

28.53 

99 

100 

96.13 

27.56 

96.00 

27.98 

95.88 

28.40 

95.76 

28.82 

100 

a! 

Q 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

i 

c 

c3 

w 

Q 

- - —, 

74 Deg. 

731 Deg. 

13k 

Deg. 

13\ Deg. 

ci 

u. 

i CL 

i 1 















































































































36 


TRAVERSE TABLE 


Distance. 

17 Deg. 

17£ Deg. 

17} Deg. 

17| Deg. 

Distance. 

Lat. 

Dep. \ 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.96 

0.29 

0.95 

0.30 

0.95 

0.30 

0.95 

0.30 

1 

2 

1.91 

0.58 

1.91 

0.59 

1.91 

0.60 

1.90 

0.61 

2 

, 3 

2.87 

0.88 

2.87 

0.89 

2.86 

0.90 

2.86 

0.91 

3 

\ 4 

3.83 

1.17 

3.82 

1.19 

3.81 

1.20 

3.81 

1.22 

4 

5 

1.78 

1.46 

4.78 

1.48 

4.77 

1.50 

4.76 

1.52 

5 

j 6 

5.74 

1.75 

5.73 

1.78 

5.72 

1.80 

5.71 

1.83 

6 

f 7 

6.69 

2.05 

6.69 

2.08 

6.68 

2.10 

6.67 

2 13 

7 

I 8 

7.65 

2.34 

7.64 

2.37 

7.63 

2.41 

7.62 

2.44 

8 

9 

8.61 

2.63 

8.60 

2.67 

8.58 

2.71 

8.57 

2.74 

9 

10 

9.56 

2.92 

9.55 

2.97 

9.54 

3.01 

9.52 

3.05 

10 

11 

10.52 

3.22 

10.51 

3.26 

10.49 

3.31 

10.48 

3.35 

11 

12 

11.48 

3.51 

11.46 

3.56 

11.44 

3.61 

11.43 

3.66 

12 

13 

12.43 

3.80 

12.42 

3.85 

12.40 

3.91 

12.38 

3.96 

13 

14 

13.39 

4.09 

13.37 

4.15 

13.35 

4.21 

13.33 

4.27 

14 

15 

14.34 

4.39 

14.33 

4.45 

14.31 

4.51 

14.29 

4.57 

15 

16 

15.30 

4.68 

15.28 

4.74 

15.26 

4.81 

15.24 

4.88 

16 

17 

16.26 

4.97 

16.24 

5.04 

16.21 

5.11 

16.19 

5.18 

17 

18 

17.21 

5.26 

17.19 

5.34 

17.17 

5.41 

17.14 

5.49 

IS 

19 

18.17 

5.56 

18.15 

5 63 

18.12 

5.71 

18.10 

5.79 

19 

20 

19.13 

5.85 

19.10 

5. 93 

19.07 

6.01 

19.05 

6.10 

20 

21 

20.08 

6.14 

20.06 

6.23 

20.03 

6.31 

20.00 

6.40 

21 

22 

21.04 

6.43 

21.01 

6 52 

20.98 

6.62 

20.95 

6.71 

22 

23 

21.99 

6.72 

21.97 

6.82 

21.94 

6.92 

21.91 

7.01 

23 

24 

22.95 

7.02 

22.92 

7.12 

22.89 

7.22 

22.86 

7.32 

24 

25 

23.91 

7.31 

23.88 

7 41 

23.84 

7.52 

23.81 

7.62 

25 

26 

24.86 

7.60 

24.83 

7.71 

24.80 

7.82 

24.76 

7.93 

26 

27 

25.82 

7.89 

25.79 

8.01 

25.75 

8.12 

25.71 

8.23 

27 

28 

26.78 

8.19 

26.74 

8.30 

26.70 

8.42 

26.67 

8.54 

28 

29 

27.73 

8.48 

27.70 

8.60 

27.66 

8.72 

27.62 

8.84 

29 

30 

28.69 

8.77 

28.65 

8.90 

28.61 

9.02 

28.57 

9.15 

30 

31 

29.65 

9.06 

29.61 

9.19 

29.57 

9.32 

29.52 

9.45 

31 

32 

30.60 

9.36 

30.56 

9.49 

30.52 

9.62 

30.48 

9.76 

32 

33 

31 .56 

9.65 

31.52 

9.79 

31.47 

9.92 

31.43 

10.06 

33 

34 

32.51 

9.94 

32.47 

10.08 

32.43 

10.22 

32.38 

10.37 

34 

35 

33.47 

10.23 

33.43 

10.38 

33.38 

10.52 

33.33 

10.67 

35 

36 

34.43 

10.53 

34.38 

10.68 

34.33 

10.83 

34.29 

10.98 

36 

37 

35.38 

10.82 

35.34 

10.97 

35.29 

11.13 

35 24 

11.28 

37 

38 

36.34 

11.11 

36.29 

11.27 

36.24 

11.43 

36.19 

11.58 

38 

39 

37.30 

11.40 

37.25 

11.57 

37.19 

11.73 

37.14 

11.89 

39 

40 

38.25 

!11.69 

38.20 

11.86 

38.15 

12.03 

38.10 

12.19 

40 

41 

39.21 

11.99 

39.16 

12.16 

39.10 

12.33 

39.05 

12.50 

41 

42 

40.16 

12.28 

40.11 

12.45 

40.06 

12.63 

40.00 

12.80 

42 

43 

41.12 

12.57 

41.07 

12.75 

41.01 

12.93 

40.95 

13.11 

43 

44 

42.08 

12.86 

42.02 

13.05 

41.96 

13.23 

41.91 

13.41 

44 

45 

43.03 

13.16 

42.93 

13.34 

42.92 

13.53 

42.86 

13.72 

45 

46 

43.99 

13.45 

43.93 

13.64 

43.87 

13.83 

43.81 

14.02 

46 

47 

44.95 

13.74 

44.89 

13.94 

44.82 

14.13 

44.76 

14.33 

47 

48 

45.90 

14.03 

45.84 

14.23 

45.78 

14.43 

45.71 

14.63 

48 

49 

46.86 

14.33 

46.80 

14.53 

46.73 

14.73 

46.67 

14.94 

49 

50 

47.82 

14.62 

47.75 

14.83 

47.69 

15.04 

47.62 

115.24 

50 

j Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 Lat. 

Distance. 

73 Deg. 

1 

72f Deg. 

72} Deg. 

722 Deg. 




















































































































TKAVEUSE table 


37 


g 

55* 

r-*- 

P 

17 Deg. 

17* Deg. 

17£ Deg. 

m 

Deg. 

KH 

• 

in 

P 

3 

O 

O 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

o 

p 

51 

48.77 

14.91 

48.71 

15.12 

48.64 

15.34 

48.57 

15.55 

51 

52 

49.73 

15.20 

49.66 ' 

15.42 

49.59 

15.64 

49.52 

15.85 

52 

53 

50.68 

15.50 

50.62 

15.72 

50.55 

15.94 

50.48 

16.16 

53 

54 

51.64 

15.79 

51.57 

16.01 

51.50 

16.24 

51.43 

16.46 

54 

55 

52.60 

16.08 

52.53 

16.31 

52.45 

16.54 

52.38 

16.77 

55 

56 

53.55 

16.37 

53.48 

16.61 

53.41 

16.84 

53.33 

17.07 

56 

57 

54.51 

16.67 

54.44 

16.90 

54.36 

17. 14 

54.29 

17.33 

57 

58 

55.47 

16.96 

55.39 

17.20 

55.32 

17.44 

55.24 

17.68 

53 

59 

56.42 

17.25 

56.35 

17.50 

56.27 

17.74 

56.10 

17.99 

59 

00 

57.38 

17.54 

57.30 

17.79 

57.22 

13.04 

57.14 

18.29 

GO 

61 

58.33 

17.83 

58.26 

18.09 

53.18 

18.34 

58.10 

18.60 

61 

62 

59.29 

18.13 

59.21 

13.39 

59.13 

18.64 

59.05 

18.90 

62 

63 

60.25 

18.42 

60.17 

13.68 

60.08 

18.94 

60.00 

19.21 

63 

64 

61.20 

18.71 1 

61.12 

18.98 

61.04 

19.25 

60.95 

19.51 

64 

65 

62.10 

19.00 | 

62.03 

19.28 

61.99 

19.55 

G1.9.1 

19.82 

65 

66 

63.12 

19.30 1 

63.03 

19.57 

62.95 

19.35 

62.86 

20 . 12 

66 

07 

64.07 

19.59 ! 

63.99 

19.87 

63.90 

20.15 

63.8 1 

20.43 

67 

68 

65.03 

19.88 

64.94 

20.16 

64.85 

20.45 

64.76 

20.73 

63 

69 

65.99 

20.17 

65.90 

20.46 

65.81 

20,75 

65.72 

21.04 

69 

70 

65.94 

20.47 

68.85 

20 .75 

66.76 

21.05 

66.67 

21.34 

70 

71 

67.90 

20.76 

67.81 

21.05 

67.71 

21.35 

67.62 

21 . 65 

71 

72 

08.85 

21.05 

68.76 

21.35 

i68.67 

21.05 

68 .57 

21.95 

72 

73 

09.81 

21.34 

69.72 

21.65 

69.62 

21.95 1 

69.52 

22.26 

73 

74 

70.77 

21.64 

70.67 

21.94 

70.58 

22.25 

70.48 

22.56 

74 

75 

71.72 

21.93 

71.63 

22.24 

71.53 

22.55 1 

71.43 

22.86 

75 

76 

72.68 

22.22 

72.53 

22.54 

i72.48 

22.85 

72.38 

23. 17 

76 

77 

73.64 

22.51 

73.54 

22.83 173.44 

23.15 

73.33 

23.47 

77 

78 

74.59 

22.80 

74.49 

23.13 | 

74.39 

23.46 

74.29 

23.78 

78 

79 

75.55 

23.10 

75.45 

23.43 

75.34 

23.76 

75.24 

24.03 

79 

80 

76.50 

23.39 

76.40 

23.72 

76.30 

24.06 

76.19 

24.39 

80 

81 

77.46 

23.68 

77.36 

24.02 

77.25 

24.36 

77.14 

24.69 

81 

82 

78.42 

23.97 

78.31 

24.32 

78.20 

24.66 

78.10 

25.00 

82 

83 

79.37 

24.27 

79.27 

24.61 

79.16 

25.96 

79.05 

25.30 

83 

84 

80.33 

24.56 

80.22 

24.91 

80.11 

25.26 

80.00 

25.61 

84 

85 

81.29 

24.85 

81.18 

25.21 

81.07 

25.56 

80.95 

25.91 

85 

86 

82.24 

25.14 

82. 13 

25.50 

82.02 

25.86 

81.91 

26.22 

86 

87 

83.20 

25.44 

83.09 

25.80 

82.97 

26.16 

82.86 

26.52 

87 

88 

84.15 

25.73 

84.04 

26.10 

83.93 

26.46 

83.81 

26.83 

88 

89 

85.11 

26.02 

85.00 

26.39 

84.88 

26.76 

84.76 

27.13 

89 

90 

86.07 

26.31 

85.95 

26.69 

85.83 

27.06 

85.72 

27.44 

90 

91 

87.02 

26.61 

86.91 

26.99 

j86.79 

27.36 

86.67 

27.74 

91 

92 

87.93 

26.90 

87.86 

27.28 

!87.74 

27.66 

87.62 

28.05 

92 

93 

88.94 

27.19 

88.82 

27.58 

88.70 

27.97 

88.57 

23.35 

93 

94 

89.89 

27.4S 

89.77 

27.87 

i89.65 

23.27 

89.53 

23.66 

94 

95 

90.85 

27.78 

90.73 

28.17 

i90.60 

28.57 

90.48 

28.96 

95 

96 

91.81 

23.07 

91.68 

28.47 

91.56 

28.87 

91.43 

29.27 

96 

97 

92.76 

28.36 

92.64 

28.76 

92.51 

29.17 

92.33 

29.57 

97 

98 

93.72 

28.65 

93.59 

29.06 

93.46 

29.47 

93.33 

29.88 

98 

99 

94.67 

28.94 

94.55 

29.36 

94.42 

29.77 

94.29 

30.18 

99 

100 

95.63 

29.24 

.95.50 

29.65 

95.37 

30.07 

95.24 

30.49 

100 

6 

o 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

i 

! Dep. 

I 

Lat. 

6 

o 

a 

♦-> 

cc 

• H 

Q 

73 Deg. 

72.f Deg. 

1 

72} 

Deg. 

72} Deg. 

d 

C/5 

. —« 















































































































38 


traverse table 


' 

Distance, j 

18 Deg - . 

18^ Deg. 

1 18| 

Deg. 

CO 

Deg. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.95 

0.31 

0.95 

0.31 

0.95 

0.32 

0.95 

0.32 

2 

1.90 

0.62 

1.90 

0.63 

1.90 

0.63 

1.89 

0.64 

3 

2.85 

0.93 

2.85 

0.94 

2 84 

I 0.95 

2.84 

0.96 | 

4 

3.80 

1.24 

3.80 

1.25 

3 79 

1.27 

3.79 

1.29 

5 

4.76 

1.55 

4.75 

1.57 

4.74 

1.59 

4.73 

1.61 

6 

5.71 

1.85 

5.70 

1.88 

5.69 

1.90 

5.6S 

1.93 1 

7 

6.66 

2.16 

6.65 

2.19 

6.64 

2.22 

6.63 

2.25 

8 

7.61 

2.47 

7.60 

2.51 

7.59 

2.54 

7.58 

2.57 

9 

8.56 

2.78 

8.55 

2.82 

8 .53 

2.86 

8.52 

2.89 

10 

9.51 

3.09 

9.50 

3.13 

9.48 

3.17 

9.47 

3.21 

11 

10.46 

3.40 

10.45 

3.44 

10.43 

3.49 

10.42 

3.54 

12 

11.41 

3.71 

11.40 

3.76 

11.38 

? 81 

11.36 

3.86 

13 

12.36 

4.02 

12.35 

4.07 

12.33 

4 12 

12.31 

4.18 

14 

13.31 

4.33 

13.30 

4.38 

13.28 

4.44 

13.26 

4.50 j 

15 

14.27 

4.64 

14.25 

4.70 

14.22 

4.76 

14.20 

4.82 

1G 

15.22 

4.94 

15.20 

5.01 

15.17 

5.0 8 

15.15 

5.14 

17 

16.17 

5.25 

16.14 

5.32 

16.12 

5.39 

16.10 

5.46 

18 

17.12 

5.56 

17.09 

5.64 

17.07 

5.71 

17.04 

5.79 

19 

18.07 

5.87 

18.04 

5.95 

18.02 

6.03 

17.99 

6.11 

20 

19.02 

6.18 

18.99 

6.26 

18.97 

6.35 

18.94 

6.43 

21 

19.97 

6.49 

19.94 

6.58 

19.91 

6.66 

19.89 

6.75 

22 

20.92 

6 .SO 

20.89 

6.89 

20.86 

6.98 

20.83 

7.07 

23 

21.87 

7.11 

21.84 

7.20 

21.81 

7.30 

21.78 

7.39 

24 

22. S3 

7.42 

22.79 

7.52 

22.76 

7.62 

22.73 

7 71 

25 

23.78 

7.73 

23.74 

7.83 

23.71 

7.93 

23.67 

8.04 

26 

24.73 

8.03 

24.69 

8.14 

24.66 

8.25 

24.62 

8.36 

27 

25.68 

8.34 

25.64 

8.46 

25.60 

8 .57 

25.57 

8.68 

28 

26.63 

8.65 

26.59 

8.77 

26.55 

8.88 

26.51 

9.00 

29 

27.58 

8.96 

27.54 

9.08 

27.50 

9.20 

27.46 

9.32 

30 

28.53 

9.27 

28.49 

9.39 

28.45 

9.52 

28.41 

9.64 

31 

29.48 

9.58 

29.44 

9.71 

29.40 

9.S4 

29.35 

9.96 

32 

30.43 

9.89 

30.39 

10.02 

30.35 

10.15 

30.30 

10.29 

33 

31.38 

10.20 

31.34 

10.33 

31.29 

10.47 

31.25 

10.61 

34 

32.34 

10.51 

32.29 

10.G5 

32.24 

10.79 

32.20 

10.93 

35 

33.29 

10.82 

33.24 

10.96 

33.19 

11.11 

33.14 

11.25 

36 

34.24 

11.12 

34.19 

11.27 

34.14 

11.42 

34.09 

11.57 

37 

35.19 

11.43 

35.14 

11.59 

35.09 

11.74 

35.04 

11.89 

38 

36.14 

11.74 

36.09 

11.90 

36.04 

12.06 

35.98 

12.21 

39 

37.09 

12.05 

37.04 

12.21 

36.98 

12.37 

36.93 

12.54 

•10 

38.04 

12.36 

37.99 

12.53 

37.93 

12.69 

37.88 

12.86 

41 j 

38.99 

12.67 

38.94 

12.84" 

38.88 

13.01 

38.82 

13.18 

42 

39.94 

12.98 

39.89 

13.15 

39.83 

13.33 

39.77 

13.50 

43 

40.90 

13.29 

40.84 

13.47 

40.78 

13.64 

40.72 

13.82 

44 1 

41.85 

13.60 

41.79 

13.78 

41.73 

13.96 

41.65 

14.14 

45 

42.80 

13.91 

42.74 

14.09 

42.67 

14.28 

42.61 

14.46 

46 

43.75 

14.21 

43.69 

14.41 

43.62 

14.60 

43.56 

14.79 

47 

44.70 

14.52 

44.64 

14.72 

44.57 

14.91 

44.51 

15.11 

48 

45.65 

14.83 

45.59 

15.03 

45.52 

15.23 

45.45 

15.43 

49 1 

46.60 

15.14 

46.54 

15.35 

46.47 

15.55 

46.40 

15.75 

50 

47.55 

15.45 

47.48 

15.06 

47.42 

15.87 

47.35 

16.07 

0) 

O 1 

d 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

-£» i 

ce 

Q | 

72 Deg. 

I 

71| Deg. 

i 

' *2 

Deg. 

1 

71} Deg. | 


niotnnpo ^COCOCOCOCOWCOCOW M n W M M W M IO W M 

LAMillia.Ioooovjoai^MMH OOOD'JOOi^ Wto^ CWCC^OOI^MM- OO 00 Cl O* >f>- Oi *3 I— © CO 00 CD Cn £. Co K> >— *93U"C1SIQ 


































































































TRAVERSE TABLE. 


39 


a 

5T 

*”► 

P 

18 Deg. 

18$ Deg. 

18j 

Deg. 

18! Deg. 

Distance. 

t 

O 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

18.50 

15.76 

48.43 

15.97 

48.36 

16.18 

48.29 

16.39 

51 

52 

49.. 45 

16.07 

49.38 

16.28 

49.31 

16.50 

49.24 

16.71 

52 

53 

50.41 

16.38 

50.33 

16.60 

50.26 

16.82 

50.19 

17.04 

53 

54 

51.36 

16.69 

51.28 

16.91 

51.21 

17.13 

51.13 

17.36 

54 

55 

52.31 

17.00 

52.23 

17.22 

52.16 

17.45 

52.08 

17.68 

55 

56 

53.26 

17.30 

53.18 

17.54 

53.11 

17.77 

53.03 

18.00 

56 

57 

54.21 

17.61 

54.13 

17.85 

54.05 

18.09 

53.98 

18.32 

57 

58 

55.16 

17.92 

55.08 

18.16 

55.00 

18.40 

54.92 

18.64 

58 

59 

56.11 

18.23 

56.03 

18.48 

55.95 

18.72 

55.87 

18.96 

59 

GO 

57.06 

18.54 

56.98 

18.79 

56.90 

19.04 

56.82 

19.29 

GO 

61 

58.01 

18 85 

57.93 

19.10 

57.85 

19.36 

! 57.76 

19.61 

61 

62 

58.97 

19.16 

58.88 

19.42 

58.80 

19.67 

' 58.71 

19.93 

62 

63 

59 . 92 

19.47 

59.83 

19.73 

59.74 

19.99 

! 59 . 66 

20.25 

63 

64 

60.87 

19.78 

60.78 

20.04 

60.69 

20.31 

60.60 

20.57 

64 

65 

61.82 

20.09 

61.73 

20.36 

61.64 

20.62 

61.55 

20.89 

65 

66 

62.77 

20.40 

62.68 

20.67 

62.59 

20.94 

62.50 

21.22 

66 

67 

63.72 

20.70 

63.63 

20.98 

63 . 54 

21.26 

63.44 

21.54 

67 

63 

64.67 

21.01 

64.58 

21.30 

64.49 

21.58 

64.39 

21.86 

68 

69 

65.62 

21.32 

65.53 

21.61 

65.43 

21.89 

65.34 

22.18 

69 

70 

66.57 

21.63 

66.48 

21.92 

66.38 

22.21 

! 66.29 

22.50 

70 

71 

67.53 

21.94 

67.43 

22.23 

67.33 

22.53 

67.23 

22.82 

71 

72 

68.48 

22.25 

68.38 

22.55 

68.28 

22.85 

, 68.18 

23.14 

72 

73 

69.43 

22.56 

69.33 

22.86 

69.23 

23.16 

69. 13 

23.47 

73 

74 

70.38 

22.87 

70.28 

23.17 

70.18 

23.48 

70.07 

23.79 

74 

75 

71.33 

23.18 

71.23 

23.49 

71.12 

23.80 

71.02 

24.11 

75 

76 

72.28 

23.49 

72.18 

23.80 

72.07 

24. i2 

71.97 

24.43 

76 

77 

73.23 

23.79 

73.13 

24.11 

73.02 

24.43 

72.91 

24.75 

77 

78 

74.18 

24.10 

74.08 

24.43 

73.97 

24.75 

73.86 

25.07 

78 

79 

75.13 

24.41 

75.03 

24.74 

74.92 

25.07 

74.81 

25.39 

79 

80 

76.08 

24.72 

75.98 

25.05 

75.87 

25.38 

75.75 

25.72 

80 

81 

77.04 

25.03 

76.93 

25.37 

76.81 

25.70 

76.70 

26.04 

81 

82 

77.99 

25.34' 

77.88 

25.68 

77.76 

26.02 

77.65 

26.36 

82 

83 

78.94 

25.65 

78.83 

25 . 99 

78.71 

26.34 

78.60 

26.08 

83 

84 

79.89 

25.96 

79.77 

26.31 

79.66 

26.65 

79.54 

27.00 

84 

85 

80.84 

26.27 

80.72 

26.62 

80.61 

26.97 

80.49 

27.32 

85 

86 

81.79 

26.58 

81.67 

26.93 

81.56 

27.29 

81.44 

27.64 

86 

87 

82.74 

26.83 

82.62 

27.25 

82.50 

27.61 

82.38 

27.97 

87 

88 

83.69 

27.19 

83.57 

27.56 

83.45 

27.92 

83.33 

28.29 

88 

89 

84.64 

27.50 

84.52 

27.87 

84.40 

28 . 24 

84.28 

28.61 

89 

90 

85.60 

27.81 

85.47 

28.18 

85.35 

28.56 

85.22 

28.93 

90 

91 

86.55 

28.12 

86.42 

28.50 

86.30 

28.87 

86.17 

29.25 

91 

92 

87.50 

28.43 

87.37 

28.81 

87.25 

29.19 

87.12 

29.57 

92 

93 

88.45 

28.74 

88.32 

29.12 

88.19 

29.51 

88.06 

29.89 

93 

94 

89.40 

29.05 

89.27 

29.44 

89.14 

•29.83 

89.01 

30.22 

94 

95 

90.35 

29.36 

90.22 

29.75 

90.09 

30.14 

89.96 

30.54 

95 

96 

91.30 

29.67 

91.17 

30.06 

91.04 

30.46 

30.91 

30.86 

96 

97 

92.25 

29.97 

92.12 

30.38 

91.99 

30.78 

91.85 

31.18 

97 

98 

93.20 

30.28 

93.07 

30.69 

92.94 

31.10 

92. SO 

31.50 

93 

99 

94.15 

30 . 59 

94.02 

31.00 

93.88 

31.41 

93.75 

31.82 

99 

100 

95.11 

30.90 

94.97 

31.32 

94.83 

31.73 

94.69 

32.14 

100 

cl 

g 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

o 

o 

a 

ed 

CO | 

3 1 

72 Deg. 

71| Deg. 

1 

74 Deg. 

71! Deg. 

w 

3 

Q 

























































































40 


TRAVERSE TABLE. 


D 
►— • 
Cft 

P 

19 Deg. 

19^ Deg. 

19£ 

Deg. 

191 Deg. 

B 

o 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

L-at. 

Dep. 

1 

0.95 

0.33 

0.94 

0.33 

0.94 

0.33 

0.94 

0.34 

2 

1.89 

0.65 

1.89 

0.66 

1.89 

0.67 

1.88 

0.68 

3 

2.84 

0.98 

2.83 

0.99 

2.83 

1.00 

2 82 

1.01 

4 

3.78 

1.30 

3.78 

1.32 

3.77 

1.34 

3.76 

1.35 

5 

4.73 

1.63 

4.72 

1.65 

4.71 

1.67 

4.71 

1.69 

6 

5.67 

1.95 

5.66 

1.98 

5.66 

2.00 

5.65 

2.03 

7 

6.62 

2.28 

6.61 

2.31 

6.60 

2.34 

6.59 

2.37 

8 

7.56 

2.60 

7.55 

2.64 

7.54 

2.67 

7.53 

2.70 

9 

8.51 

2.93 

8.50 

2.97 

8.48 

3.00 

8.47 

3.04 

10 

9.46 

3.26 

9.44 

3.30 

9.43 

3.34 

9.41 

3.38 

11 

10.40 

3.58 

10.38 

3.63 

.10.37 

3.67 

10.35 

3.72 

12 

11.35 

3.91 

11.33 

3.96 

11.31 

4.01 

11.29 

4.06 

13 

12.29 

4.23 

12.27 

4.29 

12.25 

4.34 

12.24 

4.39 

14 

13.24 

4.56 

13.22 

4.62 

13.20 

4.67 

13.18 

4.73 

15 

14.18 

4.88 

14.16 

4.95 

| 14.14 

5.01 

14.12 

5.07 

16 

15.13 

5.21 

15.11 

5.28 

15.08 

5.34 

15.06 

5.41 

17 

16.07 

5.53 

16.05 

5.60 

16.02 

5.67 

16.00 

5.74 

18 

17.02 

5.86 

16.99 

5.93 

16.97 

6.01 

16.94 

6.08 

19 

17.96 

6.19 

17.94 

6.26 

17.91 

6.34 

17.88 

0.42 

20 

18.91 

6.51 

18.88 

6.59 

18.85 

6.68 

18.S2 

6.70 

21 

19.86 

6.84 

19.83 

6.92 

19.80 

7.01 

19.76 

7.10 

22 

20.80 

7.16 

20.77 

7.25 

20.74 

7.34 

20.71 

7.43 

23 

21.75 

7.49 

21.71 

7.58 

21.68 

7.68 

21.65 

7.77 

24 

22.69 

7.81 

22.66 

7.91 

22.62 

8.01 

22.59 

8.11 

25 

23.64 

8.14 

23.60 

8.24 

23.57 

8.35 

23.53 

8.45 

26 

24.58 

8.46 

24.55 

8.57 

24.51 

8.68 

24.47 

8 .79 

27 

25.53 

8.79 

25.49 

8.90 

25.45 

9.01 

25.41 

9.12 

28 

26.47 

9.12 

26.43 

9.23 

26.39 

9.35 

26.35 

9.46 

29 

27.42 

9.44 

27.38 

9.56 

27.34 

9.68 

27.29 

9.80 

30 

28.37 

9.77 

28.32 

9.89 

28.28 

10.01 

28.24 

10.14 

31 

29.31 

10.09 

29.27 

10.22 

29.22 

10.35 

29.18 

10.48 

32 

30.26 

10.42 

30.21 

10.55 

30.16 

10.68 

30.12 

10.81 

33 

31.20 

10.74 

31.15 

10.88 

31.11 

11.02 

31.06 

11.15 

34 

32.15 

11.07 

32.10 

11.21 

32.05 

11.35 

32.00 

11.49 

35 

33.09 

11.39 

33.04 

11.54 

32.99 

11.68 

32.94 

11.83 

36 

34.04 

11.72 

33.99 

11.87 

33.94 

12.02 

33.88 

12.17 

37 

34.98 

12.05 

34.93 

12.20 

34.88 

12.35 

34.82 

12.50 

38 

35.93 

12.37 

35.88 

12.53 

35.82 

12.68 

35.76 

12.84 

39 

36.88 

12.70 

36.82 

12.86 

36.76 

13.02 

36.71 

13.18 

40 

37.82 

13.02 

37.76 

13.19 

37.71 

13.35 

37.65 

13.52 

41 

38.77 

13.35 

38.71 

13.52 

38.65 

13.69 

38.59 

13.85 

42 

39.71 

13.67 

39.65 

13.85 

39.59 

14.02 

39.53 

14.19 

43 

40.66 

14.00 

40.60 

14.18 

40.53 

14.35 

40.47 

14.53 

44 

41.60 

14.32 

41.54 

14.51 

41.48 

14.69 

41.41 

14.87 

45 

42.55 

14.65 

42.48 

14.84 

42.42 

15.02 

42.3*5 

15.21 

46 

43.49 

14.98 

43.43 

15.17 

43.36 

15.36 

43.29 

15.54 

47 

44.44 

15.30 

44.37 

15.50 

44.30 

15.69 

44.24 

15.88 

48 

45.38 

15.63 

45.32 

15.83 

45.25 

16.02 

1 45 . 18 

16.22 

49 

46.33 

15.95 

46.26 

16.15 

46.19 

16.36 

j 46.12 

16.56 

50 

47.28 

16.28 

47.20 

16.48 

47.13 

16.69 

47.06 

16.90 

© 

u 

e 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

| Distn 

71 Deg. 

70f Deg. 

70| Deg. 

70.| Deg. 


Uisiancc.j |otCvO“.}OiO'<^coK»>~-'|ocDOD~.}cscnif-cois2>- j |oooo*v}a5 0Ti^o;K)K-|ocooo-<ja5cn ( f».coto | ‘aouc^siQ 



























































































41 


TRAVERSE TABLE. 


D 

• 

U1 

19 Deg. 

191 

Deg. 

19f 

Dog. 

19J Deg. 

O 
►— • 

75 

«■* 

P 

3 

O 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

O 

o 

51 

48.22 

16.60 

48.15 

16 .81- 

48.07 

17.02 

48.00 

17.23 

51 

52 

49.17 

16.93 

49.09 

17.14 

49.02 

17.36 

48.94 

17.57 

52 

53 

50.11 

17.26 

50.04 

17.47 

49.96 

17.69 

49.88 

17.91 

53 

54 

51.06 

17.58 

50.98 

17.80 

50.90 

18.03 

50.82 

18.25 

54 

55 

52.00: 

17.91 

51.92 

18.13 

51.85 

18.36 

51.76 

18.59 j 

55 

58 

52.95 

18.23 

52.87 

18.46 

52.79 

18.69 

52.71 

18.92 

56 

57 

53.89 

18.56 | 

53.81 

18.79 

53.73 

19.03 

53.65 

1 9.26 

57 

58 

54.84 

18.83 

54.76 

19.12 

54.67 

19.36 

54.59 

19.60 

58 

59 

55.79 

19.21 

55.70 

19.45 

55.62 

19.69 

55.53 

19.94 

59 

00 

56.73 

19.53 

56.65 

19.78 

56.56 

20.03 

56.47 

20.27 

GO 

61 

57.68 

19.86 

57.59 

20.11 

57.50 

20.36 

57.41 

20.61 

61 

62 

58.62 

20.19 

58.53 

20.44 

58.44 

20.70 

58.35 

20,95 

62 

63 

59.57 

20.51 

59.48 

20.77 

59.39 

21.03 

59.29 

21.29 

63 

64 

60.51 

20.84 

60.42 

21.10 

60.33 

21.36 

60.24 

21.63 

64 

65 

61.46 

21.16 

61.37 

21 .43 

61.27 

21.70 

61.18 

21.96 

65 

66 

62.40 

21.49 

62.31 

21.76 

62.21 

22.03 

62.12 

22.30 

66 

67 

63.35 

21.81 

63.25 

22.09 

63.16 

22.37 

63.06 

22.64 

67 

68 

64.30 

22.14 

64.20 

22.42 

64.10 

22.70 

64.00 

22 .9S 

68 

69 

65.24 

22 .4G 

65.14 

22.75 

65.04 

23.03 

64.94 

23.32 

69 

70 

C6.19 

22.79 

66.09 

23.08 

65.98 

23.37 

65.88 

23.65 

70 

71 

67.13 

23.12 

67.03 

23.41 

66.93 

23.70 

96.82 

23.99 

71 

72 

G8.08 

23.44 

67.97 

23.74 

67.87 

24.03 

67.76 

24.33 

72 

73 

69.02 

23.77 

68.92 

24.07 

68 .SI 

24.37 

68.71 

24.67 

73 

74 

69.97 

24,09 

69.86 

24.40 

69.76 

24.70 

69.65 

25.01 

74 

75 

70.91 

24.42 

70.81 

24.73 

70.70 

25.04 

70.59 

25.34 

75 

76 

71.86 

24.74 

71.75 

25.06 

71.64 

25.37 

71.53 

25.68 

76 

77 

72.80 

25.07 

72.69 

25.39 

72.58 

25.70 

72.47 

26.02 

77 

78 

73.75 

25.39 

73.64 

25.72 

73.53 

20.04 

73.41 

26.33 

78 

79 

74.70 

25.72 

74.58 

26.05 

74.47 

26.37 

74.35 

26.70 

79 

80 

75.64 

26.05 

75.53 

26.38 

75.41 

26.70 

75.29 

27.03 

80 

81 

76.59 

26.37 

76.47 

26.70 

76.35 

27.04 

76.24 

27.37 

81 

82 

77.53 

26.70 

77.42 

27.03 

77.30 

27.37 

77.18 

27.71 

82 

83 

78.48 

27.02 

78.36 

27.36 

78.24 

27.71 

78.12 

28.05 

83 

84 

79.42 

27.35 

79.30 

27.69 

79.18 

28.04 

79.06 

28.39 

84 

85 

80.37 

27.67 

80.25 

28.02 

80.12 

28.37 

80.00 

28.72 

85 

86 

81.31 

28.00 

81.19 

28.35 

81.07 

28.71 

80.94 

29.06 

86 

87 

82.26 

28.32 

82.14 

28.68 

82.01 

29.04 

81.88 

29.40 

87 

88 

83.21 

28.65 

83.08 

29.01 

92.95 

29.37 

82.82 

29.74 

88 

89 

84.15 

28.98 

84.02 

29.34 

83.90 

29.71 

83.76 

30.07 

89 

90 

85.10 

29.30 

84.97 

29.67 

84.84 

30.04 

84.71 

30.41 

90 

91 

86.04 

29.63 

85.91 

30.00 

85.78 

30.38 

85.65 

30.75 

91 

92 

86.99 

29.95 

86.86 

30.33 

86.72 

30.71 

86.59 

31.09 

92 

93 

87.93 

30.28 

87.80 

30.66 

87.07 

31.04 

87.53 

31.43 

93 

94 

88 . S8 

30.60 

88.74 

30.99 

88.61 

31.38 

88.47 

31.76 

94 

95 

89.82 

30.93 

89.69 

31.32 

89.55 

31.71 

89.41 

32.10 

95 

96 

90.77 

31.25 

90.63 

31.65 

90.49 

32.05 

90.35 

32.44 

96 

97 

91.72 

31.58 

91.58 

31.98 

91.44 

32.38 

91.29 

32.78 

97 

98 

92.66 

31.91 

92.52 

32.31 

92.38 

32.71 

92.24 

33.12 

98 

99 

93.61 

32.23 

93.46 

32.64 

93.32 

33.05 

93.18 

33.45 

99 

100 

94.55 

32.56 

94.41 

32.97 

94.26 

33.38 

94.12 

33.79 

100 

d 

o 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

O 

o 

c 

a 

«-> 

w 

•—4 

Q 

71 Deg. 

701 Deg. 

70i 

Deg. 

701 Deg. 

■4-t 

co 

Q 

J 











































































































42 


traverse table 


1 Distance.1 

L 


20 Deg 


T 

20} Deg. 


20^ 

Deg. 

20} Deg. 

C 

5)’ 

(—* 

P 

o 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0 

.94 

0 

34 

0 

.94 

0.35 

0 

.94 

0.35 

0 

.94 

0.35 

1 

2 

1 

.88 

0 

6S 

1 

.88 

0.69 

1 

.87 

0.70 

1 

.87 

0.71 

2 

3 

2 

.82 

1 

03 

2 

.81 

1.04 

2 

.81 

1.05 

2 

.81 

1.06 

3 

4 

3 

.76 

1 

37 

3 

.75 

1.38 

3 

.75 

i .40 

3 

.74 

1.42 

4 

5 

4 

.70 

1 

71 

4 

.69 

1.73 

4 

.68 

1.75 S 

4 

.68 

1.77 

5 

G 

5 

.04 

2. 

05 

5 

.63 

2.08 

5 

.62 

2.10 

5 

.61 

2.13 

6 

7 

6 

.58 

2. 

39 

6 

.57 

2.42 

6 

.56 

2.45 

6 

. 55 

2.48 

7 

8 

7 

.52 

O 

V 

74 

7 

.51 

2.77 

7 

.49 

2.80 1 

7 

.48 

2.83 

8 

9 

8 

.46 

O 

u 

08 

8 

.44 

3.12 

8 

.43 

3.15 

8 

.42 

3.19 

9 

10 

9 

.40 

3. 

42 

9 

.38 

3.46 

9 

.37 

3.50 

9 

.35 

3.54 

10 

11 

10 

.34 

3. 

76 

10 

.32 

3.81 

10 

.30 

3.85 

10 

.29 

3.90 

11 

12 

11 

.28 

4. 

10 

11 

.26 

4.15 

11 

.24 

4.20 

11 

.22 

4.25 

12 

13 

12 

.22 

4. 

45 

12 

.20 

4.50 

12 

.18 

4.55 

12 

. 16 

4.61 

13 

14 

13 

. 16 

4. 

79 

13 

.13 

4.85 

13 

.11 

4.90 

13 

.09 

4.96 

14 

15 

14 

. 10 

5. 

13 

14 

.07 

5.19 

14 

.05 

5.25 

14 

.03 

5.31 

15 

16 

15 

.04 

5. 

47 

15 

.01 

5.54 

14 

.99 

5.60 

14 

.96 

5.67 

16 

17 

15 

.97 

5. 

81 

15 

.95 

5.88 

15 

.92 

5.95 

15 

.90 

6.02 

17 

18 

16 

.91 

6. 

16 

1G 

.89 

6.23 

16 

.86 

6 ; 30 

16 

.83 

6.38 

18 

19 

17 

.85 

0. 

50 

17 

.83 

6.58 

17 

.80 

6.65 

17 

.77 

6.73 

19 

20 

13 

.79 

6. 

84 

18 

.76 

6.92 

18 

.73 

7.00 

18 

.70 

7.09 

20 

21 

19 

.73 

7. 

18 

19 

.70 

7.27 

19 

.67 

7.35 

19 

.64 

7.44 

21 

22 

20 

.07 

7. 

52 

20 

.64 

7.61 

20 

.61 

7.70 

20 

.57 

7.79 

— * 

23 

21 

.01 

7. 

87 

21 

.58 

7.96 

21 

.54 

8.05 

21 

.51 

8. 15 

23 

«> 1 

22 

.55 

8. 

21 

22 

.52 

8.31 

22 

.48 

8.40 

22 

.44 

8.50 

24 

25 

23 

.49 

8. 

55 

23 

.45 

8.65 

23 

.42 

8.76 

23 

.38 

8.86 

25 

26 

24 

.43 

8. 

89 

24 

.39 

9.00 

24 

.35 

9.1 1 

24 

.31 

9.21 

26 

27 

25 

.37 

9. 

23 

25 

.33 

9.35 

25 

.29 

9.46 

25 

.25 

9.57 

27 

28 

26 

.31 

9. 

58 

26 

.27 

9.69 

26 

.23 

9.81 

26 

. 18 

9.92 

28 

29 

27 

.25 

9. 

92 

27 

.21 

10.04 

27 

.16 

10.16 

27 

.12 

10.27 

29 

30 

28 

.19 

10. 

26 

28 

15 

10.38 

28 

.10 

10.51 

28 

.05 

10.63 

30 

31 

29 

13 

10. 

GO 

29 

.08 

10.73 

29 

.04 

10.86 

28 

.99 

10.98 

31 

32 

30 

.07 

10. 

94 

30 

.02 

11.08 

29 

.97 

11.21 

29 

.92 

11.34 

32 

33 

31 

.01 

11. 

29 

30 

.96 

11.42 

30 

.91 

11.56 

30 

.86 

11.69 

33 

34 

31 

.95 

11. 

63 

31 

.90 

11.77 

31 

.85 

11.91 

31 

.79 

12.05 

34 

35 

32 

.89 

11. 

97 

32 

.84 

12.11 

32 

.78 

12.26 

32 

.73 

12.40 

35 

36 

33 

.83 

12. 

31 

33 

.77 

12.46 

33 

.72 

12.61 

33 

. 66 

12.75 

36 

37 

31 

.77 

12. 

65 

34 

.71 

12.81 

34 

.66 

12.96 

34 

.60 

13.11 

37 

38 

35 

.71 

13. 

00 

35 

65 

13.15 

35 

.59 

13.31 

35 

.54 

13.46 

38 

39 

36 

.65 

13. 

34 

36 

.59 

13.50 

36 

.53 

13.66 

36 

.47 

13.82 

39 

40 

37 

.59 

13. 

68 

37 

.53 

13.84 

37 

.47 

14.01 

37 

.41 

14.17 

40 

41 

38 

.53 

14. 

02 

38 

.47 

14.19 

38 

.40 

14.36 

38 

.34 

14.53 

41 

42 

39 

.47 

14. 

36 

39 

.40 

14.54 

39 

.34 

14.71 

39 

.28 

14.88 

42 

43 

40 

.41 

14. 

71 

40 

.3'1 

14.88 

40 

.28 

15.06 

40 

.21 

15.23 

43 

44 

41 

.35 

15. 

05 

41 

.28 

15.23 

41 

.21 

15.41 

41 

.16 

15.59 

44 

45 

42 

.29 

15. 

39 

i 42 

.22 

15.58 

42 

.15 

15.76 

42 

.08 

15.94 

45 

46 

43 

.23 

15. 

73 

43 

.16 

15.92 

43 

.09 

16.11 

43 

.02 

16.30 

46 

47 

44 

.17 

16. 

07 

44 

.09 

16.27 

44 

.02 

16.46 

43 

.95 

16.65 

47 

48 

45 

.11 

16. 

42 

45 

.03 

16.61 

44 

.96 

16.81 

44 

.89 

17.01 

48 

49 

46 

.04 

1G. 

76 

45 

.97 

16.96 

45 

.90 

17.16 

45 

.82 

17.36 

49 

50 

46 

.98 

17. 

10 

46 

.91 

17.31 

46 

.83 

17.51 

46 

.76 

17.7i 

50 

6 

V 

c 

rJ 

Q 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

J Lat. 

Distance. 

70 Deg. 

69} Deg. 



Deg. 

69} Deg. 


















































































































TRAVERSE TABLE 


43 


a 
►— • 

00 

*-► 

P 

20 Deg. 

20$ Deg. 

20^ Deg. 

20f Deg. 

5 

cr* 

3 

o 

a> 

Lat. 

Dep. 

Lat. 

Dep. 

Lcit* 

Dep. 

Lat. 

Dep. 

o 

CD 

51 

47.92 

17.44 

47 .35 

17.65 

47.77 

17.86 

47.69 

18.07 

51 

52 

48.86 

17.79 

48.79 

18.00 

48.71 

18.21 

48.63 

18.42 

52 

53 

49.80 

18.13 

49.72 

18.34 

49.64 

18.56 

49.56 

13.78 

53 

54 

50.74 

18.47 

50.66 

13.69 

50.58 

18.91 

50.50 

19. 13 

54 

55 

51.68 

18.81 

51.60 

19.04 

51.52 

19.26 

51.43 

19.49 

55 

56 

52.62 

19.15 

52.54 

19.38 

52.45 

19.61 

52.37 

19.84 

56 

57 

53.56 

19.50 

53.48 

19.73 

53.39 

19.96 

53.30 

20.19 

57 

58 

54.50 

19.84 

54.42 

20.07 

54.33 

20.31 

54.24 

20.55 

58 

59 

55.44 

20.18 

55.35 

20.42 

55.26 

20.66 

55.17 

20.90 

59 

60 

56.39 

20.52 

56.29 

20.77 

56.20 

21.01 

56.11 

21.26 

60 

61 

57.32 

20.86 

57.23 

21.11 

57.14 

21.36 

57.04 

21.61 

61 

62 

58.26 

21.21 

58.17 

21.46 

58.07 

21.71 

57.98 

21 .97 

62 

63 

59.20 

21.55 

59.11 

21.81 

59.01 

22.06 

58.91 

22.32 

63 

64 

60.14 

21.89 

60.04 

22.15 

59.95 

22.41 

59.85 

22.67 

64 

65 

61.08 

22.23 

60.98 

22.50 

60.83 

22.76 

60.78 

23 . 03 

65 

66 

62.02 

22.57 

61.92 

22.84 

61.82 

23.11 

61.72 

23.38 

66 

67 

62.96 

22.92 1 

62.86 

23.19 

62.76 

23.46 

62.65 

23.74 

67 

68 

63.90 

23.26 

63.80 

23.54 

63.69 

23.81 

63.59 

24.09 

68 

69 

64.84 

23.60 

64.74 

23.83 

64.63 

24.16 

64.52 

24.45 

69 

70 

65.78 

23.94 

65.67 

24.23 

65.57 

24.51 

65.46 

| 

24.80 

70 

71 

66.72 

24.28 

66.61 

24.57 

66.50 

24.86 

66.39 

25.15 

71 

72 

67.66 

24.63 

67.55 

24.92 

67.44 

25.21 

67.33 

25.51 

72 

73 

68.60 

24.97 

63.49 

25.27 

68.33 

25.57 

68.26 

25.86 

73 

74 

69.54 

25.31 

69.43 

25.61 

69.31 

25.92 

69.20 

26.22 

74 

75 

70.48 

25.65 

70.36 

25.96 

70.25 

26.27 

70.14 

26.57 

75 

76 

71.42 

25.99 

71.30 

26.30 

71.19 

26.62 

71.07 

26.93 

76 

77 

72.36 

26.34 

72.24 

26.65 

72.12 

26.97 

72.01 

27.28 

77 

78 

73.30 

28.68 

73.18 

27.00 

73.06 

27.32 

•72.94 

27.63 

78 

79 

74.24 

27.02 

74.12 

27.34 

74.00 

27.67 

73.88 

27.99 

79 

80 

75.18 

27.36 

75.06 

27.69 

74.93 

28.02 

74.81 

28.34 

80 

SI 

76.12 

27.70 

75.99 

28.04 

75.87 

28.37 

75.75 

28.70 

81 

82 

77.05 

28.05 

76.93 

28.33 

76.81 

28.72 

76.68 

29.05 

82 

83 

77.99 

28.39 

77.87 

28.73 

77.74 

29.07 

77.62 

29.41 

83 

84 

78.93 

28.73 

78.81 

29.07 

78.68 

29.42 

78.55 

29.76 

84 

85 

79.87 

129.07 

79.75 

29.42 

79.62 

29.77 

79.49 

30.11 

85 

86 

80.81 

29.41 

80.63 

29.77 

80.55 

30.12 

80.42 

30.47 

86 

87 

81.75 

29.76 

81.62 

30.11 

81.49 

30.47 

81 .36 

30.82 

87 

88 

82.69 

30.10 

82.56 

30.46 

82.43 

30.82 

82.29 

31.18 

88 

89 

83.63 

30.44 

83.50 

30.80 

83.36 

31.17 

83.23 

31.53 

89 

90 

84.57 

30.78 

84.44 

31.15 

84.30 

31.52 

84.16 

31.89 

90 

91 

85.51 

31.12 

85.33 

31.50 

85.24 

31.87 

85.10 

32.24 

91 

92 

86.45 

31.47 

86.31 

31.84 

86.17 

32.22 

86.03 

32.59 

92 

93 

87.39 

31.81 

87.25 

32.19 

87.11 

32.57 

86.97 

32.93 

93 

94 

83.33 

! 32.15 

83.19 

32.54 

88.05 

32.92 

87.90 

33 /SO 

94 

95 

89.27 

32.49 

89.13 

32.38 

88.98 

33.27 

88.84 

33.66 

95 

96 

90.21 

32.83 

90.07 

33.23 

89.92 

33.62 

89.77 

34.01 

96 

97 

91.15 

33.18 

91.00 

33.57 

90.86 

33.97 

90.71 

34.37 

97 

98 

92.09 

33.52 

91.94 

33.92 

91.79 

34.32 

91.64 

34.72 

98 

99 

93.03 

33.86 

92.88 

34.27 

92.73 

34.67 

92.58 

35.07 

99 

100 

93.97 

34.20 

93.82 

34.61 

93.67 

35.02 

93.51 

35.43 

100 

6 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

I Lat. 

6 

o 

r* 

cd 

r/i 

• 

70 Deg. 

69f Deg. 

69^ 

1 

Deg. 

691 Deg 

u. 

5 




























































































































TRAVERSE TABLE. 


44 


o 

ST 

<—■ 

P 

21 Deg. 

21i Deg. 

1 

21| Deg. 

21| Deg. 

O 

t/. 

c-* 

P 

3 

O 

n 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

G 

o 

CD 

1 

0.93 

0.36 

0.93 

0.36 

0.93 

0.37 

0.93 

0.37 

1 

2 

1.87 

0.72 

1.86 

0.72 

1.86 

0.73 

1.86 

0.74 

2 

3 

2.80 

1.08 

2.80 

1.09 

2.79 

1.10 

2.79 

1.11 

3 

4 

3.73 

1.43 

3.73 

1.45 

3.72 

1.47 

3.72 

1 .48 

4 

6 

4.07 

1.79 

4.66 

1.81 

4.65 

1.83 

4.64 

1 .85 

5 

G 

5.00 

2.15 

5.59 

2.17 

5.58 

2.20 

5.57 

2.22 

6 

7 

0.54 

2.51 

6.52 

2.54 

6.51 

2.57 

6.50 

2.59 

7 

8 

7.47 

2.87 

7.46 

2.90 

7.44 

2.93 

7.43 

2.96 

8 

( J 

8.40 

3.23 

8.39 

3.26 

8.37 

3.30 

8.36 

3.34 

9 

10 

9.34 

3.58 

9.32 

3.62 

9.30 

3.67 

9.29 

3.71 

10 

11 

10.27 

3.94 

10.25 

3.99 

10.23 

4.03 

10.22 

4.08 

11 

12 

11.20 

4.30 

11.18 

4.35 

11.17 

4.40 

11.15 

4.45 

12 \ 

13 

12.14 

4.66 

12.12 

4.71 

12.10 

4.76 

12.07 

4.82 

13 

14 

13.07 

5.02 

13.05 

5.07 

13.03 

5.13 

13.00 

5.19 

14 

15 

14.00 

5.38 

13.98 

5.44 

13.96 

5.50 

13.93 

5 . 56 

15 

10 

14.94 

5.73 

14.91 

5.80 

14.89 

5.86 

14.86 

5.93 

16 

17 

15.87 

6.09 

15.84 

6.16 

15.82 

0.23 

15.79 

6.30 

17 

18 

10.80 

0.45 

16.78 

6.52 

16.75 

6.60 

16.72 

6.67 

18 

19 

17.74 

6.81 

17.71 

6.89 

17.68 

6.96 

17.65 

7.04 

19 

20 

18.07 

7.17 

18.64 

7.25 

18.61 

7.33 

18.58 

7.41 

20 

21 

19.61 

7.53 

19.57 

7.61 

19.54 

7.70 

19.50 

7.78 

21 

22 

20.54 

7.88 

20.50 

7.97 

20.47 

8.06 

20.43 

8.15 

22 

23 

21.47 

8.24| 

21.44 

8.34 

21.40 

8.43 

21.36 

8.52 

23 

24 

22.41 

8.60 

! 22.37 
23.30 

8.70 

22.33 

8.80 

22.29 

8.89 

24 

25 

23.34 

8.96 

9.06 

23.26 

9.16 

23.22 

9.26 

25 

20 

24.27 

9.32 

24.23 

9.42 

24.19 

9.53 

24.15 

9.63 

26 

27 

25.21 

9.68 

25.10 

9.79 

25.12 

9.90 

25.08 

10.01 

27 

28 

20.14 

10.03 

20.10 

10.15 

26.05 

10.26 

26.01 

10 38 

28 

29 

27.07 

10.39 

27.03 

10.51 

20.98 

10.63 

26.94 

10.75 

29 

30 

28.01 

10.75 

27.96 

10.87 

27.91 

11.00 

27.88 

11.12 

30 

31 

28.94 

11.11 

28.89 

11.24 

28.84 

11.36 

28.79 

11.49 

31 

32 

29.87 

11.47 

29.82 

11.60 

29.77 

11.73 

29.72 

11.86 

32 

33 

30.81 

11.83 

30.76 

11.96 

30.70 

12.09 

30.65 

12.23 

33 

34 

31.74 

12.18 

31.69 

12.32 

31.63 

12.46 

31.58 

12.60 

34 

35 

32.68 

12.54 

32.62 

12.69 

32.56 

12.83 

32.51 

12.97 

35 

30 

33.61 

12.90 

33.55 

13.05 

33.50 

13.19 

33.44 

13.34 

36 

37 

34.54 

13.26 

34.48 

13.41 

34.43 

13.56 

34.37 

13.71 

37 

38 

35.48 

13.62 

35.42 

13.77 

35.36 

13.93 

35.29 

14.08 

38 

39 

36.41 

13.98 

36.35 

14.14 

36.29 

14.29 

36.22 

14.45 

39 

40 

37.34 

14.33 

37.28 

14.50 

37.22 

14.68 

37.15 

14.82 

40 

41 

38.28 

14.69 

38.21 

14.86 

38.15 

15.03 

38.08 

15.19 

41 

42 

39.21 

15.05 

39.14 

15.22 

39.08 

15.39 

39.01 

15.56 

42 

43 

40.14 

41X18 

15.41 

40.08 

15.58 

40.01 

15.76 

39.94 

15.93 

43 

44 

15.77 

41.01 

15.95 

40.94 

16.13 

40.87 

16.30 

44 

45 

42.01 

16.13 

41.94 

16.31 

41.87 

16.49 

41.80 

16.68 

45 

46 

42.94 

16.48 

42.87 

16.67 

42.80 

16.86 

42.73 

17.05 

46 

47 

43.88 

16.84 

43.80 

17.03 

43.73 

17.23 

43.65 

17.42 

47 

48 

44.81 

17.20 

44.74 

17.40 

44.66 

17.59 

44.58 

17.79 

48 

49 

45.75 

17.56 

45.67 

17.76 

45.59 

17.96 

45.51 

18.16 

49 

50 

40.68 

17.92 

46.60 

18.12 

46.52 

18.33 

46.44 

18.53 

50 

• 

© 

© 

G 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Q 

O 

C 

eg 

1/5 

• 

a 

09 Deer. 

o 

63$ Deg 

G8i 

Deg. 

68 $ Deg. 

cd 

w 

C/3 

» —4 

-fj 









































































































t_kav.eii.se table 


45 


o 

cc 

P 

21 Deg. 

• 

21] Deg. 

* 

■ 21A Deg. 

21] Deg. i 

Distance.] 

i 

D 

o 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dop. 

Lat. 

Dep. 1 

51 

47.61 

18.28 

47.53 

1S.4S 

47.45 

18.69 

47.37 

18.90 j 

51 

52 

48.55 

18.64 

48.46 

18.85 

48.38 

19.06 

48.30 

19.27 

52 

53 

49.48 

18.99 

49.40 

19,21 

49.31 

19.42 

49.23 

19.64 

53 

54 

50.41 

19.35 

50.33 

19.57 

50.24 

19.79 

50.16 

20.01 

54 

55 

51.35 

19.71 

51.26 

19.93 

51.17 

20.16 

51.08 

20.38 | 

55 

58 

52 28 

20.07 

52.19 

20.30 

52.10 

20.52 

52.01 

20.75 

56! 

57 

53 21 

20.43 

53.12 

20.66 

53.03 

20.89 

52.94 

21.12 

57 5 

58 

54.15 

20.79 

54.06 

21.02 

53.96 

21.26 

53.87 

21.49 

58 

59 

55.08 

21.14 

54.99 

21.38 

54.89 

21.62 

54.80 

21.86 

59 

GO 

56.01 

21.50 

55.92 

21.75 

55.83 

21.99 

55.73 

22.23 

60 

61 

56.95 

21.86 

56.85 

22.11 

56.76 

22.36 

56.66 

22.60 

61 

62 

57.88 

22.22 

57.78 

22.47 

57.69 

22.72 

57.59 

22.97 

62 

63 

58.82 

22.58 

58.72 

22,83 

58.62 

23.09 

58.52 

23.35 

63 

64 

59.75 

22.94 

59.65 

23.20 

59.55 

23.46 

59.44 

23.72 

64 

65 

60.68 

23.29 

60.58 

23.56 

60.48 

23.82 

60.37 

24.09 

65 

66 

61.62 

23.65 

61.51 

23.92 

61.41 

24.19 

61.30 

24.46 

66 

67 

62.55 

24.01 

62.44 

24.28 

62.34 

24.56 

62.23 

24.83 i 

67 

68 

63.48 

24.37 

63.38 

24.65 

63.27 

24.92 

63.16 

25.20 

68 

69 

64.42 

24.73 

64.31 

25.01 

64.20 

25.29 

64.09 

25.57 

69 

70 

65.35 

25.09 

65.24 

25.37 

;65.13 

i 

25.66 

65.02 

25.94 

70 

7) 

66.28 

25.44 

66.17 

25.73 

166.06 

26.02 

65.95 

26.31 

71 

72 

67.22 

25.80 

67.10 

26. 10 

66.99 

26.39 

66.87 

26.68 

72 

73 

68.15 

26.16 

68.04 

26.46 

67.92 

26.75 

67.80 

27.05 

73 

74 

69.08 

26.52 

68.97 

26.82 

68.85 

27.12 

68.73 

27.42 

74 

75 

70.02 

26.88 

69.90 

27.18 

69.78 

27.49 

69.66 

27.79 

75 

76 

70.95 

27.24 

70.83 

27.55 

70.71 

27.85 

70.59 

28.16 

76 

77 

71.89 

27.59 

71.76 

27.91 

71.64 

28.22 

71.52 

28.53 

77 

78 

72.82 

27.95 

72.70 

28.27 

72.57 

28.59 

72.45 

28.90 

78 

79 

73.75 

28.31 

73.63 

28.63 

73.50 

28.95 

73.38 

29.27 

79 

80 

74.69 

28.67 

74.56 

29.00 

74.43 

29.32 

74.30 

29.64 

80 

81 

75.62 

29.03 

75.49 

29.38 

75.36 

29.69 

75.23 

30.02 

81 

82 

76.55 

29.39 

76.42 

29.72 

76.29 

30.05 

76.16 

30.39 

82 

83 

77.49 

29.74 

77.36 

30.08 

77.22 

30.42 

77.09 

30.76 

83 

84 

78.42 

30.10 

78.29 

30.44 

78.16 

30.79 

78.02 

31.13 

84 

85 

79.35 

30.46 

79.22 

30.81 

79.09 

31.15 

78.95 

31.50 

85 

86 

80.29 

30.82 

80.15 

31.17 

|80.02 

31.52 

79.88 

31.87 

86 

87 

81.22 

31.18 

81.08 

31.53 

80.95 

31.89 

80.81 

32.24 

87 

88 

82.16 

31 54 

82.02 

31.89 

81.88 

32.25 

!81.74 

32.61 

88 

89 

83.09 

31.89 

82.95 

32.26 

82.81 

32.62 

82.66 

32.98 

89 

90 

84.02 

32.25 

83.88 

32.62 

83.74 

32.99 

!83.59 

33.35 

SO 

■91 

84.96 

32.61 

84.81 

32.98 

84.67 

33.35 

|84.52 

33.72 

91 

n 92 

85.89 

32.97 

85.74 

33.34 

j 85.60 

33.72 

85.45 

34-09 

92 

93 

86.82 

33.33 

86.68 

33.71 

86.53 

34.08 

86.38 

34.46 

93 

94 

87.76 

33.69 

87.61 

34.07 

!| 87.46 

34.45 

87.31 

34.83 

94 

95 

88.69 

34.04 

88.54 

34.43 

: 88.39 

84.82 

188.24 

35.20 

95 

96 

89.62 

34.40 

89.47 

34.79 

!89.32 

35.18 

!89.17 

35.57 

I 96 

97 

90.56 

34.76 

90.40 

35.16 

90.25 

35.55 

!| 90.09 

35.94 97 

98 

91.49 

35.12 

91.34 

|35.52 

94.18 

35.92 

|| 91.02 

36.31 

98 

99 

92.42 

35.43 

92.27 

135.88 

92.11 

36.28 

!j 91.95 

36.69 

: 99 

100 

93.36 

35.84 

93.20 

36.24 

93.04 

36.65 

|92.88 

37.06 

: 100 

6 

o 

G 

Dop. 

Lat. 

Dep. 

j Lat. 

Dep. 

l| 

Lat. 

Dep. 

Lat. 

0 

o 

73 

ao 

Ca 

69 .Dec. 

o 

68 ] Deg. 

i| 

6 P,i 

i| 

Deg. 

63] Dog. 

V. 


22 














































































































46 


TRAVERSE TABLE. 


3 

CO* 

r* 

P 

P 

o 

p 

22 Deg. 

22\ Deg. 

22^ 

Deg. 

22\ 

Deg. 

5 

5* 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

a 

1 

‘ 0.93" 

0.37 

0.93 

0.38 

9.92 

0.38 

0.92 

0.39 

1 

2 

1.85 

0.75 

1.85 

0.76 

1.85 

0.77 

1.84 

0.77 

2 

3 

2.78 

1.12 

2.78 

1.14 

2.77 

1.15 

2.77 

1.16 

3 

4 

3.71 

1.50 

3.70 

1.51 

3.70 

1.53 

3.69 

' .55 

4 

5 

4.64 

1.87 

4.63 

1.89 

4.62 

1.91 

4.61 

i . 93 

5 

6 

5.56 

2.25 

5.55 

2.27 

5.54 

2.30 

5.53 

2.32 

6 

7 

6.49 

2.62 

6.48 

2.65 

6.47 

2.68 

6.46 

2.71 

7 

8 

7.42 

3.00 

7.40 

3.03 

7.39 

3.06 

7.38 

3.09 

8 

9 

8.31 

3.37 

8.33 

3.41 

8.31 

3.44 

8.30 

3.48 

9 

10 

9.27 

3.75 

9.26 

3.79 

9.24 

3.83 

9.22 

3.87 

10 

11 

10.20 

4.12 

10.18 

4.17 

10.16 

4.21 

10.14 

4.25 

11 

12 

11.13 

4.50 

11.11 

4.54 | 

11.09 

4.59 

11.07 

4.64 

12 

13 

12.05 

4.87 

12.03 

4.92 

12.01 

4.97 

11.99 

5.03 

13 

14 

12.98 

5.24 

12.96 

5.30 

12.93 

5.36 

12.91 

5.41 

14 

15 

13.91 

5.62 

13.88 

5.68 

13.86 

5.74 

13.83 

5.80 

15 

16 

14.83 

5.99 

14.81 

6.06 

14.78 

6. 12 

14.76 

6.19 

16 

17 

15.76 

6.37 

15.73 

6.44 

15.71 

6.51 

15.68 

6.57 

17 

18 

16.69 

6.74 

16.66 

6.82 

16.63 

6.89 

16.60 

6.96 

18 

19 

17.62 

7.12 

17.59 

7. 19 

17.55 

7.27 

17.52 

7.35 

19 

20 

18.54 

7.49 

18.51 

7.57 

18.48 

7.65 

18.44 

7.73 

20 

21 

19.47 

7.87 

19.44 

7.95 

19.40 

8.04 

19.37 

8.12 

21 

22 

20.40 

8.24 

20.36 

8.33 

20.33 

8.42 

20.29 

8.51 

99 

A* Ad 

23 

21.33 

8.62 

21.29 

8.71 

21.25 

8.80 

21.21 

8.89 

23 

24 

22.25 

8.99 

22.21 

9.09, 

22. 17 

9.18 

22.13 

9.28 

24 

25 

23.18 

9.37 

23.14 

9.47 

23.10 

9.57 

23.05 

9.67 

25 

26 

24.11 

9.74 

24.06 

9.84 ; 

24.02 

9.95 

23.98 

10.05 

26 

27 

25.03 

10.11 

24.99 

10.22 

24.94 

10.33 1 

24.90 

10.44 

27 

2S 

25.96 

10.49 

25.92 

10.60 

25.87 

10.72 I 

,25.82 

10.83 

28 

2*3 

26.89 

10.86 

26.84 

10.98 

26.79 

11.10! 

126.74 

11.21 

29 

30 

27.82 

11.24 

27.77 

11.36 

27.72 

11.48 

|27.07 

11.60 

30 

31 

28.74 

11.61 

28.69 

11.74 

28.64 

11.86 1 

j 28.59 

11.99 

31 

32 

29.67 

11.99 

29.62 

12.12 

29.56 

12.25 | 

29.51 

12.37 

32 

33 

30.60 

12.36 

30.54 

12.50 

30.49 

12.63 1 

S 30.43 

12.76 

33 

34 

31.52 

12.74 

31 .47 

12.87 

31.41 

13.01 

[31.35 

13.15 

34 

35 

32.45 

13.11 

32.39 

13.25 

32.34 

13.39 

32.28 

13.53 

35 

36 

33.33 

13.49 

33.32 

13.63 

33.26 

13.78 

33.20 

13.92 

36 

37 

34.31 

13.86 

34.24 

14.01 

34.18 

14.16 

|34 . 12 

14.31 

37 

38 

35.23 

14.24 

35.17 

14.39 

35.11 

14.54 

35.04 

14.70 

38 

39 

36.16 

14.61 

36.10 

14.77 

36.03 

14.92 

35.97 

15.08 

39 

40 

37.09 

14.98 

37.02 

15.15 

36.96 

15.31 

36.89 

15.47 

40 

41 

38.01 

15.36 

37.95 

15.52 

37.88 

15.69 

37.81 

15.88 

41 

42 

38.94 

15.73 

33.87 

15.90 

38.80 

16.07 

38.73 

16.24 

42 

43 

39.87 

16.11 

39.80 

16.23 

39.73 

16.46 

39.65 

16.63 

43 

44 

40.80 

16.48 

40.72 

16.66 

40.65 

16.84 

40.58 

17.02 

44 

4o 

41.72 

16.86 

41.65 

17.04 

41.57 

17.22 

41.50 

17.40 

45 

46 

42.65 

17.23 

42.57 

17.42 

12.50 

17.60 

42.42 

17.79 

46 

47 

43.58 

17.61 

43.50 

17.80 

43.42 

17.99 

43.34 

18.18 

47 

48 

<14.50 

17.98 

44.43 

18.18 

44.35 

18.37 

44.27 

18.56 

4S 

49 

45.43 

18.36 

45.35 

18.55 

45.27 

18.75 

45.19 

18.95 

49 

60 

46.36 

18.73 

46.28 

18.93 

46.19 

19.13 

46.11 

19.34 

50 

• 

o 

o 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lilt* 

Dep. 

Lat. 

o 

o 

<-< 

C/3 

I s 

63 Deg. 

67f Deg. 

67£ Deg. 

67* Deg. 

• H 

! Q 

I 


















































































































TKAVEKSE TABLE. 


47 


1 

a 

M* 

P 

22 Deg. 

22} Deg. 

221 Deg. 

221 Deg. 

Distance. 

3 

n 

a 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dcp. 

Lat. 

Dcp. 

51 

47.29 

19.10 

47.20 

J9.31 

47. 12' 

19.52 

47.03 

19.72 

51 

r >2 

48.21 

19.48 

48.13 

19.09 

48.04 

19.90 

47.95 

20.11 

52 

53 

49. 14 

1 9.85 

49.05 

20.07 

48.97 

20.28 

48.88 

20.59 

53, 

54 

50.07! 

20.20 

49.98 

20.45 

49.89 

20.60 

49.80 

20.88 i 

54/ 

55 

51.00 

20.00 

50.90 

20.83 

50.81 

21.05 

50.72 

21.27 ! 

5 

55 

51.92 

20.98 

51. S3 

21.20 

5 l. 74 

21.40 

51.64 

21.66 

56 

57 

52.85 

21.05 | 

52.76 

21.58 

5:4.66 

21.81 

52.57 

22.04j 

57 

58 

50.78 

21.73 

50.68 

21.90 

50.59 

22.20 

53.49 

22.40 ( 

58 

50 

54.70 

22. 10 

54.6 l 

22.34 

51.51 

22.58 

5 4.41 

22.82 

59 

00 

55.00 

22.48 

55.50 

22.72 

55.40 

22.06 

55.33 

20.20 

60 

61 

56.50 

22.85 

56.47 

20.10 

50.06 

20.0 l 

50.25 

20.59 

61 

62 

57.49 

20.20 

57.38 

20.48 

57.28 

23.73 

57. 13 

23.93 

62 

00 

58.41 

20.60 

58.31 

20.85 

58 • 20 

2 4.11 

58.10 

24.36 

60 

04 

59.04 

20.97 

59.23 

24.23 

59. 10 

2 4.49 

59.02 

24.75 

64 

6f> 

00.27 

24.35 

60.10 

21.61 

GO. 05 

2 4.87 j 

59.94 

25. 1 4 

65 

GO 

01.19 

24.72 

61.09 

24.99 

60.98 

25.26 

60.87 

25.52 

66 

07 

62. 12 

25.10 

62.01 

25.07 

61.90 

25.6 4 

61 .79 

25.9 L 

67 

68 

60.05 

25.47 

62.94 

) • / • ) 

62.82 

26.02 

62.71 

26.30 

63 

69 

00.98 

25.85 

63.86 

26.13 

60.75 

20.41 

60. GO 

26.68 

69 

70 

04.90 

•Mi 9‘~> 

64.79 

20.51 

64.67 

26.70 

64.55 

27.07 

70 

71 

05.80 

26.60 

65.71 

20.88 

65.60 

27.17 

65.48 

27.46 

71 

72 

00.76 

20.9 7 

06.64 

27.20 

65 52 

27.55 

66.40 

27.84- 

72 

70 

67.68 

27.35 

07.50 

27.64 

67.44 

27.94 

67.02 

23.20 

70 

74 

08.61 

27.72 

03.49 

28.02 

63.07 

28.02 

08.24 

28.62 

74 

75 

09.54 

28. 10 

69.42 

28.40 

69.29 

23.70 

69. 17 

29.00 

75 

70 

70.47 

28.47 

70.34 

23.78 

70.21 

29.08 

70.09 

29.09 

76 

77 ! 7!.09 

28.84 

71.27 

29. 10 

71.14 

29.47 

71.01 

29.78 

77 

78 

72.02 

29.22 

!72.19 

29.53 

72.06 

29.85 

' 7!.90 

30. 16 

78 

79 

70.25 

29.59 

i73.12 

29.91 

72.99 

0 ). 20 

| 72.85 

00.55 

70 

80 

74.17 

29.97 

j 74.04 

00.29 

70.91 

00.6 l 

j 70.78 

00.94 

80 

81 

75.10 

00.01 

74.97 

30.67 

74.83 

01.00 

|74.70 
75.62 

0 1.02 

81 

82 

70.00 

00.72 

75.89 

0 l. 05 

75.76 

01 .08 

01.71 

82 

80 

70.90 

01 .09 

/0.82 

31 .43 

76.68 

01.76 

76.54 

02. 10 

80 

81 

77.88 

01.47 

77.75 

31.81 

77.61 

02.15 

1 77.46 

32.43 

84 

85 

78.81 

01.84 

78.67 

02.19 

78.50 

02.50 

178.09 

02.87 

85 

80 

79.74 

32.22 

79.00 

02.56 

79.45 

02.91 

I 70.01 

00.26 

Sfi 

87 

80.66 

32.59 

80.52 

02.94 

80.38 

00.29 

!80.20 

00.6 4 

87 

88 

81.59 

02.97 

81.45 

30.02 

8 1.30 

00.63 

81.15 

3 4.03 

88 

80 

82.52 

33.34 

82.37 

00.70 

82.20 

0 4.06 

!82.08 

3 4.42 

89 

90 

80.45 

00.71 

80.30 

04.08 

80. 15 

31.44 

j 80.00 

04.80 

90 

91 

84.07 

04.09 

34.22 

34.46 

81.07 

3 4.82 

j 80.92 

05.19 

91 

92 

85.00 

34.46 

85. 15 

3 l. 84 

85.00 

35.21 

184.84 

35.58 

92 

90 

86.20 

34.84 

86.03 

35.21 

85.92 

05.59 

I 85.76 

35.96 

| 90 

94 

87.16 

35.21 

87.00 

35.59 

86.84 

- 05.9 7 

186.60 

36.0:) 

91 

95 

83.08 

05.59 

87.93 

35.97 

87.77 

06.35 

|87.61 

06.74 

95 

96 

89.01 

05.96 

88.85 

36.05 

88.69 

35.7 4 

33.50 

37. 12 

96 

97 

89.94 

36.34 

89.78 

35.70 

89.62 

37.12 

89.45 

137.51 

97 

93 

90.80 

36.71 

90.70 

07. 11 

90.54 

37.50 

90. OS 

37.90 

i 98 

99 

91.79 

07.09 

91.60 

37.49 

1 91.46 

37.89 

91.00 

1 08.28 

99 

100 

92.72 

37.46 

92.55 

07.86 

• 92.09 

38.27 

92.22 

103.67 

: 100 

d 

o 

s 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

Dep. 

Lat. 

\ • 

1 cl 

1 o 

1 e 

w 

5 

68 Deg. 

67| Deg. 

C7i 

Deg. 

67J Deg. 

C3 

l w 

i 73 

5 

J 



































































































48 


TIIAVEKSE TABLE. 


1 

S| 
a ! 

P 

23 Deg. 

23} Deg. 

23i 

/ 

Deg. 

23} Deg. 

D 

ST 

r-*- 

P 

3 

o 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep/» 

Lat. 

Dep. 

P 

o 

CD 

1 

0.92 

0.39 

0.92 

0.39 

0.92 

0.40 

0.92 

0.40 

l 

2 

1.84 

0.78 

1.84 

0.79 

1.83 

0.80 

1.83 

0.81 

2 

3 

2.76 

1.17 

2.76 

1.18 

2.75 

1.20 

2.75 

1.21 

3 

4 1 

3.68 

1.56 

3.68 

1.58 

3.67 

1.59 

3.66 

1.61 

1 

5 

4.60 

1.95 

4.59 

1.97 

4.59 

1.99 

4.58 

2.01 

5 

j 6 | 

6.52 

2.34 

5.51 

2.37 

5.50 

2.39 

5.49 I 

2.42 

6 

j 7 j 

6.44 | 

2.74 

6.43 

2.76 

6.42 

2.79 

6.41 

2.82 

7 

8 

7.36 

3.13 

7.35 

3.16 

7.34 

3.19 

7.32 , 

3.22 

8 

9 

8.28 1 

3.52 

S. 27 

3.55 

8.25 

3.59 

8.24 

3.62 

9 

10 

9.20 

3.91 

9.19 

3.95 

9.17 

3.99 

9.15 i 

4.03 

10 

11 

10.13 

4.30 

10.11 

4.34 

10.09 

4.39 

10.07 | 

4.43 

i i 

12 

11.05 

4.69 

11.03 

4.74 

11.00 

4.78 

10.98 ! 

4.83 

12 

13 

11.97 

5.08 

11.94 

5.13 

11.92 

5.18 

11.90 : 

5.24 

13 

14 

12.89 

5.47 

12.86 

5.53 

12.84 

5.58 

12.81 

5.64 

14 

15 

13.81 

5.86 

13.78 

5.92 

13.76 

5.98 

13.73 

6.04 

15 

16 

14.73 

6.25 

14.70 

6.32 

14.67 

6.38 

14.64 

6.44 

16 

17 

15.65 

6.64 

15.62 

6.71 

15.59 

6.78 

15.56 

6.85 

17 

18 

16.57 

7.03 

16.54 

7.11 

16.51 

7.18 

16.48 

7.25 

18 

19 

17.49 

7.42 

17.46 

7.50 

17.42 

7.58 

17.39 

7.65 

19 

20 

18.41 

7.81 

18.38 

7.89 

18.34 

7.97 

18.31 

8.05 

20 

21 

19.33 

8.21 

19.29 

8.29 

19.26 

8.37 

19.22 

8.46 

21 

22 

20.25 

8.60 

20.21 

8.68 

20.18 

8.77 

20.14 

8.86 

22 

23 

21.17 

8.99 

21.13 

9.08 

21.09 

9.17 

21.05 

9.26 

23 

24 

22.09 

9.38 

22.05 

9.47 | 

22.01 

9.57 1 

21.97 

9.67 

24 

25 

23.01 

9.77 

22.97 

9.87 1 

22.93 

9.97 

22.88 

10.07 

25 

26 

23.93 

10.16 

23.89 

10.26 

23.84 

10.37 1 

23.80 

10.47 

26 

27 

24.85 

10.55 1 

24.81 

10.60 

24.76 

10.77 

24.71 

10.87 

27 

28 

25.77 

10.94 | 

25.73 

11.05 

25.68 

11.16! 

25.63 

l.l .28 

23 

29 

26.69 

11.33 

26.64 

111.45 I 

26.59 

11.56 

26.54 

11.68 

29 

30 

27.62 

11.72 

27.56 

1 11.84 

27.51 

11.96 | 

27.40 

12.08 

30 

31 

28.54 

12.11 

28.48 

12.24 

28.43 

12.36 

28.37 

12.49 

31 

32 

29.46 

12.50 

29.40 

12.03 

29.35 

12.76 

29.29 

12.89 

3,2 

33 

30.38 

12.89 

30.32 

13.03 

30.26 

13.16 

30.21 

13.29 

33 

34 

31.30 

13.28 

31.24 

13.42 

31.18 

13.56 

31.12 

13.69 

34 

35 

32.22 

13.68 

32.16 

13.82 

32.10 

13.96 

32.04 

14.10 

35 

36 

33.14 

14.07 

33.08 

14.21 

33.01 

14.35 

j 32.95 

14.50 

36 

37 

34.08 

14.46 

34.00 

14.61 

33.93 

14.75 

33.87 

14.90 

37 

38 

34.98 

14.85 

34.91 

15.00 

34.85 

15.15 

I34.78 

15.30 

38 

39 

35.90 

15.24 

35.83 

15.39 

35.77 

15.55 

35.70 

15.71 

39 

40 

36.82 

15.63 

36.75 

15.79 

36.68 

15.95 

36.61 

16.11 

40 

41 

37.74 

16.02 

37.67 

16.18 

37.60 

16.35 

37.53 

16.51 

41 

42 

38.66 

16.41 

38.59 

16.58 

38.52 

16.75 

33.44 

16.92 

42 

43 

39.58 

16.80 

39.51 

16.97 

39.43 

17.15 

39.36 

1 17.32 

43 

44 

40.50 

17.19 

40.43 

17.37 

40.35 

17.54 

40.27 

17.72 

44 

45 

41.42 

17.58 

41.35 

j 17.76 

41.27 

17.94 

41.19 

18.12 

45 

46 

42.34 

17.97 

42.26 

18.16 

42.18 

18.34 

42.10 

13.53 

46 

47 

1 43.26 

18.36 

43.18 

;18.55 

43.10 

18.74 

43.02 

18.93 

47 

48 

!44.18 

18.76 

44.10 

18.95 

44.02 

19.14 

43.93 

19.33 

48 

49 

1 45.10 

19.15 

j 45.02 

19.34 

44.94 

19.54 

44.85 

19.73 

49 

50 

46.03 

19.54 

45.94 

| 19.74 

45.85 

19.94 

145.77 

20.14 

50 

© 

o 

c 

Dep. 

Lat. 

Dop. 

j Lat. 

Dep. 

Lat. 

I; Dep. 

•Lat. 

c5 

o 

! ci 

in 
• «■* 

P 

1 

: 67 Deg 

66} Deg. 

; 66£ 

h 

Deg. 

Ij 

66} Deg. 

d 

*-> 

1 .2 

P 

I 











































































































TRAVERSE TABLE 


•19 


3 

5T 

r+ 

P 

23 Deg. 

23} Deg. 

23 j 

Deg. 

23} Deg. 

a 
►— • 

rn 

p 

3 

o 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

! Dep. 

hZ5 

o 

p 

51 

46.95 

19.93 

46.86 

20. 13 

46.77 

20.34 

46.68 

20.54 

51 

52 

47.87 

20.32 

47.78 

20.53 

47.69 

20.73 

47.60 

20.94 

52 

5:5 

48.79 

20.71 

48.70 

20.92 

48.60 

21.13 

48.51 

21.35 

53 

1 54 

49.71 

21.10 

49.61 

21.32 

49.52 

21.53 

49.43 

21.75 

54 

1 55 

50.63 

21.49 

50.53 

21.71 

50.44 

21.93 

50.34 

22.15 

55 

j 56 

51.55 

21.83 

51.45 

22.11 

51.36 

22.33 

51.26 

22.55 

56 

K 57 

52.47 

22.27 

52.37 

22.50 

52.27 

22.73 

52.17 

22.96 

57 

1 53 

53.39 

22.86 

53.20 

22.90 

53.19 

23.13 

53.09 

23.36 

58 

| 53 

54.31 

23.05 

54.21 

23.29 

54.11 

23.53 

54 00 

23.76 

59 

\ 60 

55.23 

23.44 

55.13 

23.63 

55.02 

23.92 

54.92 

24.16 

60 

; 61 

56.15 

23.83 

56.05 

24.03 

55.94 

24.32 

55.83 

24.57 

61 

62 

57.07 

24.23 

56.97 

24.47 

56.86 

24.72 

56.75 

24.97 

62 

63 

57.99 

24.62 

57.88 

24.87 

57.77 

25.12 

57.66 

25.37 

63 

61 

58.91 

25.01 

58.80 

25.26 

58.69 

25.52 

58.58 

25.78 

64 

65 

59.83 

25.40 

59.72 

25.66 

59.61 

25.92 

59,50 

26. 18 

65 

66 

60.75 

25.79 

GO. 64 

26.05 

60.53 

26.32 

60.41 

26.58 

66 

67 

61.67 

26.18 

61.56 

26.45 

61.44 

26.72 

61.33 

26.98 

67 

63 

62.59 

26.57 

62.48 

26.84 

62.36 

27.11 

62.24 

27.39 

68 

69 

03.51 

23.98 

63.40 

27.24 

63.23 

27.51 

63.16 

27.79 

69 

70 

64.44 

27.35 

64.32 

27.63 

64.19 

27.91 

61.07 

23.19 

70 

71 

65.36 

27.74 

65.23 

23 ..03 

65.11 

28.31 

64.99 

23.59 

71 

72 

66.23 

23.13 

66.15 

28.42 

66.03 

28.71 

65.90 

29.00 

72 

73 

67.20 

28.52 

67.07 

28.82 

66.95 

29.11 

66.32 

29.40 

73 

74 

63. 12 

28.91 

67.99 

29.21 

67.86 

29.51 

67.73 

29.80 

74 

75 

69.04 

29.30 

68.91 

29.61 

68.78 

29.91 

63.65 

30.21 

75 

76 

69.93 

29.70 

69.83 

30.00 j 

69.70 

;30.30 

69.56 

30.61 

76 

77 

70.88 

30.09 

70.75 

30.40 

70.61 

30.70 

70.48 

31.01 

77 

78 

71.80 

30.48 

ri.67 

30.79 

71.53 

31.10 

71.39 

31.41 

73 

79 

72.72 

39.87 

72.58 

31.18 

72.45 

31.50 

72.31 

31.82 

79 

80 

73.64 

31.26 

73.50 

31.58 

73.35 

31.90 

73.22 

32.22 

80 

81 

74.56 

31.65 

74.42 

31.97 

74.28 

32.30 

74.14 

32.62 

81 

82 

75.48 

32.04 

75.34 

32.37 

75.20 

32.70 

75.06 

33.03 

82 

83 

76.40 

32.43 

76.26 

32.76 

76.12 

33.10 

75.97 

33.43 

83 

84 

77.32 

32.82 

77.18 

33.16 

77.03 

33.49 

76.89 

33.83 

84 

85 

78.21 

33.21 

78.10 

33.55 

77.95 

33.89 

77.80 

34.23 

85 

86 

79.16 

33.60 

79.02 

33.95 

78.87 

34.29 

78.72 

34.64 

86 

87 

SO.03 

33.99 

79.93 

34.34 

79.78 

34.69 

79.63 

35.04 

87 

83 

81 .00 

31.33 

80.85 

34.74 

80.70 

35.09 

80.55 

35.44 

88 

89 

81.92 

34.78 

81.77 

35.13 

81.62 

35.49 

81.46 

35.84 

89 

90 

82.85 

35.17 

82.69 

35.53 

82.54 

35.89 

82.33 

36.25 

90 

S 91 

83.77 

35.56 

83.61 

35.92 

83.45 

36.29 

83.29 

36.65 

91 

1 92 

84.69 

35.95 

84.53 

36.32 

84.37 

36.68 

84.21 

37.05 

92 

§ 93 

85.61 

36.34 

85.45 

36.71 

85.29 

37.03 

85.12 

37.46 

93 

94 

86.53 

36.73 

86.37 

37.11 

86.20 

37.43 

86.01 

37.86 

94 

95 

87.45 1 

37.12 

87.29 

37.50 

87.12 

37.88 

86.95 

38.26 

95 

96 

83.37 | 

37.51 

88.20 

37.90 

88.04 

33.28 [ 

87.87 

38.66 

98 

97 

89.29 ! 

37.90 

89.12 

38.29 

88.95 

33.68 

83.79 

39.07 

97 

98 

90.21 | 

38.29 

90.04 

33.68 

89.87 

39.03 

89.70 

39.47 

98 

99* 

91.13 

33.68 

90.96 

39.03 

90.79 

39.48 

90.62 

39.87 

99 

100 

92.05 | 

39.07 

91.88 

39.47 

91.71 | 

39.87 

91.53 

40.27 

100 

o 

o 

£ ! 

Dep. 

L & t« 

Dep. 

Lat. 

Dep. 

Lat. 

Dep 

Lat, 

o’ 

o 

c 

co 

3 

67 Deg. 

66f Deg. 

66i Deg. 

66} Deg. 

CO 
. >*■« 

Q 




































































































60 


TRAVERSE TAULK 


o 

r C * 
£9 

24 Deg. 

*24} Deg. 

24} 

Deg. 

24} Deg. 

C 

5T 

*-* 

P 

3 

O 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lai. 

Dep. 

Lat. 

Dep. 

o 

cr> 

l 

0.91 

0.41 

0.91 

0.41 

0.91 

0.41 

0.91 

0.42~ 

i 

2 

1.83 

0.81 

1.82 

0.82 

1.82 

0.83 

1.82 

0.84 

o 

*•> 

3 

2.74 

j 1.22 

2.74 

1.23 

2.73 

1.24 

2.72 

1.26 

3 

4 

3.65 

1.63 

3.65 

1.64 

3.64 

1.66 

3.63 

1.67 

4 

5 

4.57 

2.03 

4.56 

2.05 

4.55 

2.07 

4.54 

2.09 

5 

6 

5:48 

2.44 

5.47 

2.46 

5.46 

2.49 

5.45 

2.51 

6 

7 

6.39 

2.85 

6.38 

2.87 

6 .37 

2.90 

6.36 

2 .93 

7 

8 

7.31 

3.25 

7.29 

3.29 

7.28 

3.32 

7.27 

3.35 

8 

9 

8.22 

3.66 

8.21 

3.70 

8.19 

3.73 

8.17 

3.77 

9 

10 

9.14 

4.07 

9.12 

4.11 

9.10 

4.15 

9. OS 

4.19 

10 

11 

10.05 

4.47 

10.03 

4.52 

10.01 

4.56 

9.99 

4.61 

11 

12 

10.96 

4.88 

10.94 

4.93 

10.92 

4.98 

10.90 

5.02 

12 

13 

11.88 

5.29 

1 1.85 

5.34 

1 1.83 

5.39 

11.81 

5.44 

13 

14 

12.79 

5.69 

12.76 

5.75 

12.74 

5.8i | 

12.71 

5.86 

14 

15 

13.70 

6.10 

13.68 

6.16 

13.65 

6.22 

13.62 

6.28 

15 

16 

14.62 

6 .5 1 

14.59 

6.57 

14.56 

6.64 l 

14.53 

/ 6.70 

16 

17 

15.53 

6.92 

1 5.50 

6.98 

15.47 

7.05 

15.44 

7. 12 

17 

18 

16.44 

7.32 

16.41 

7.39 

16.38 

7.46 

16.35 

7.54 

18 

19 

i 7.36 

7.73 

17.32 

7.80 

17.29 

7.88 

17.25 

7.05 

19 

20 

18.27 

8.13 

18.24 

8.21 

18.20 

8.29 

18.16 

8 .37 

20 

21 

19.18 

8.54 

19.15 

8.63 

19.11 

8.71 j 

19.07 

8 .79 

21 

22 

20.10 

8 . 95 

20.06 

9.04 

20.02 

9.12 

19.98 

9.21 

22 

23 

21.01 

9.35 

20.97 

9.45 

20.93 

9.54 

20.89 

9.63 

23 

24 

21.93 

9.76 

21.83 

9.86 

21 .84 

9.95 

21.80 

10.05 

24 

25 

22.84 

10.17 

22.79 

10.27 

22.75 

10.37 

22.70 

10.47 

25 

26 

23.75 

10.58 

23.7k 

10.68 

23.66 

10.78 

23.61 

10.89 

26 

27 

24.67 

10.98 

24.02 

11.09' 

24.57 

1 1 .20 

24.52 

1 1 .30 

27 

28 

25.58 

11.39 

25.53 

11.50 

25.48 

11.61 

25.43 

11.72 

28 

29 

26.49 

11.80 

26.44 

11.91 

26.39 

12.03 

26.34 

12. 14 

29 

39 

27.41 

12.20 

27.35 

12.32 

27.30 

12.44 

27.24 

12.56 

30 

31 

28.32 

12.61 

28.26 

12.73 

28.21 

12.86 

28.15 

12.98 

31 

32 

29.23 

13.02 

29. 18 

13. 14 

29.12 

13.27 

29.06 

13.40 

32 

33 

30.15 

13.42 

30.09 

13.55 

30.03 

13.68 

29.97 

13.82 

33 

34 

31.06 

13.83 

31.00 

13.96 

30.94 

14.10 

30.83 

14.23 

34 

35 

31.97 

14.24 

31.91 

14.3S 

31.85 

14.51 

31.78 

14.65 

35 

36 

32.89 

14.64 

32.82 

14.79 

32.76 

14.93 

32.69 

15.07 

36 

37 

33.80 

15.05 

33.74 

15.20 

33.67 

15.34 

33.60 

15.49 

37 

38 

34.71 

15.46 

34.65 

15.61 

34.58 

15.76 

34.51 

15.91 

38 

39 

35.63 

15.86 

35.56 

16.02 

35.49 

16.17 

35.42 

16.33 

39 

40 

30.54 

16.27 

36.47 

16.43 

36.40 

16.59 

36.33 

16.75 

40 

41 

37.46 

16.68 ' 

37.38 

16.84 

37.31 

17.00 

37.23 

17.16 

41 

42 

38.37 

17.03 

33.29 

17.25 

38.22 

17.42 

38.14 

17.58 

42 

43 

39.28 

17.49 

39.21 

17.66 

39.13 

17.83 

39.05 

18.00 

43 

44 

40.20 

17.90 

40.12 

18.07 

40.04 

18.25 

39.96 

18.42 

44 

45 

41.11 

18.30 

41.03 

18.48 

40.95 

18.66 

40.87 

18.84 

45 

46 

42.02 

18.71 

41.94 

18.89 

41.86 

19.08 

41.77 

19.26 

46 

47 

42.94 

19.12 

42.85 

19.30 

42.77 

19.49 

42.68 

19.68 

47 

48 

43.85 

19.52 

4-3.76 

19.71 

43.68 

19.91 

43.59 

20.10 

48 

49 

44.76 

19.93 

44.68 

20.13 

44.59 

20.32 

44.50 

20.51 

49 

50 j 

45.68 

20.34 

45.59 

20.54 

45.50 

20.73 

45.41 

20.93 

50 

6 1 

2 1 
C i 

Dep. ! 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

CD 

V 

r* 

rt 

*-» 1 

■Jj , 

Q 

66 Deg. 

i 

65f Deg. 

65^ Deg. 

65} Deg. 

ri 

*-> 

T. 

s 

























































































TRAVERSE TAELE. 


51 


o 

v>* 

C-f 

p 

24 Deg. 

24J Deg. 

24} Deg. 

24f Deg. 

o 
►— • 

Vl 

r—t- 

P 

3 

o 

p 

Licit* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

o 

51 

46.59 

20.74 

46.50 

20.95 

46.41 

21.15 

46.32 

21.35 

51 

52 

47.50 

21.15 

47.41 

21.36 

47.32 

21.56 

47.22 

21 .77 

52 

53 

48.42 

21.56 

48.32 

21.77 

48.23 

21.98 

48.13 

22.19 

53 

54 

49.33 

21.96 

49.24 

22.18 

49.14 

22.39 

49.04 

22.61 

54 

55 

50.24 

22.37 

50.15 

22.59 

50.05 

22.81 

49.95 

23.03 

55 

56 

51.16 

22.78 

51.06 

23.00 

50.96 

23.22 

50.86 

23.44 

56 

57 

52.07 

23.18 

51.97 

23.41 

51.87 

23.64 

51.76 

23.86 

57 

58 

52.99 

23.59 

52.88 

23.82 

52.78 

24.05 

52.67 

24.28 

58 

50 

53.90 

24.00 

53.79 

24.23 

53.69 

24.47 

53.58 

24.70 

59 

GO 

54.81 

24.40 

54.71 

24.64 

54.60 

24.88 

54.49 

25.12 

60 

61 

55.73 

24.81 

55.62 

25.05 

55.51 

25.30 

55.40 

25.54 

61 

G2 

56.64 

25.22 

56.53 

25.46 

56.42 

25.71 

56.30 

25.96 

62 

63 

57.55 

25.62 

57.44 

25.88 

57.33 

26.13 

57.21 

25.38 

63 

64 

58.47 

26.03 

58.35 

26.29 

58.24 

26.54 

58.12 

26.79 

64 

65 

59.38 

26.44 

59.26 

26.70 

59.15 

26.96 

59.03 

27.21 

65 

66 

00.29 

26.84 

60.18 

27.11 

60.06 

27.37 

59. S4 

27.63 

66 

67 

61.21 

27.25 

61.09 

27.52 

60.97 

27.78 

60.85 

28.05 

67 

68 

62.12 

27.66 

62.00 

27.93 

61.88 

28.20 

61.75 

28.47 

63 

60 

63.03 

23.08 

62.91 

28.34 

62.79 

28.61 

62.66 

28.89 

69 

70 

63.95 

23.47 

63.82 

23.75 

63.70 

29.03 

63.57 

29.31 

70 

71 

64.86 

28.88 

64.74 

29.16 

64.61 

29.44 

04.48 

29.72 

71 

72 

65.78 

29.28 

65.65 

29.57 

65.52 

29.86 

65.39 

30.14 

72 

73 

66.69 

29.69 

66.56 

29.98 

66.43 

30.27 

66.29 

30.56 

73 

74 

67.60 

30.10 

67.47 

30.39 

67.34 

30.69 

67.20 

30.93 

74 

75 

68.52 

30.51 

68.38 

30.80 

68.25 

31.10 

68.11 

31.40 

75 

76 

69.43 

30.91 

6.9.29 

31.21 

69.16 

31.52 

!69.02 

31.82 

76 

77 

70.34 

31.32 

70.21 

31.63 

70.07 

31.93 

!69.93 

32.24 

77 

78 

71.26 

31.73 

71.12 

32.04 

70.98 

32.35 

70.84 

32.66 

78 

70 

72.17 

32.13 

72.03 

32.45 

71.89 

32.76 

j71.74 

33.07 

79 

80 

73.03 

32.54 

72.94 

32.86 

72.80 

33. IS 

72.65 

33.49 

80 

81 

74.00 

32.95 

73.85 

33.27 

73.71 

33.59 

73.56 

33.91 

81 

82 

74.91 

33.35 

74.76 

33.68 

74.62 

34.00 

74.47 

34.33 

82 

83 

75.82 

33.76 

75.68 

34.09 

75.53 

34.42 

75.38 

34.75 

83 

84 

76.74 

34.17 

76.59 

34.50 

76.44 

34.83 

76.28 

35.17 

84 

85 

77.65 

34.57 

77.50 

34.91 

77.35 

35.25 

77.19 

35.59 

85 

86 

78.56 

34.98 

78.41 

35.32 

78 26 

35.66 

78.10 

36.00 

86 

87 

79.48 

35.39 

79.32 

35.73 

79.17 

36.08 

79.01 

36.42 

87 

83 

80.39 

35.79 

80.24 

36.14 

80.08 

36.49 

79.92 

36.84 

88 

89 

8 J .31 

36.20 

81.15 

36.55 

80.99 

36.91 

80.82 

37 26 

39 

90 

82.22 

36.61 

82.06 

36.96 

81.90 

37.32 

81.73 

37.68 

90 

91 

83.13 

37.01 

82.97 

37.38 

82.81 

37.74 

82.64 

33.10 

91 

92 

84.05 

37.42 

83.83 

37.79 

83.72 

38.15 

83.55 

38.52 

92 

93 

84.96 

37.83 

84.79 

38.20 

84.63 

38.57 

84.46 

38.94 

93 

94 

85.87 

33.23 

85.71 

38.61 

85.54 

38.98 

85.37 

39.35 

94 

95 

86.79 

38.64 

86.62 

39.02 

86.45 

39.40 

86.27 

39.77 

95 

i 96 

87.70 

39.05 | 

87.53 

39.43 

87.36 

39.81 

87.18 

40.19 

96 

97 

88.61 

39.45 j 

88.44 

39.84 

88.27 

40.23 

88.09 

40.61 

97 

98 

89.53 

39.86 1 

89.35 

40.25 

89.18 

40.64 

89.00 

41.03 

98 

99 

90.44 

40.27 

90.26 

40.66 

90.09 

41.05 

89.91 

41.45 

99 

100 

91.35 

40.67 

91.18 

41.07 

91.00 

41.47 

90.81 

41.87 

100 

a> 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

c 

r* 

** 

a 

p 

68 Dec. 

65f Deg. 

65} Deg. 

65} Deg. 

a 

cc 

5 





































































































'Di<?fnnr'p ^NCO^iOfflNOOGO ^ N « rjuc «D N 00 OS O -csm^iOONOOOC ^ CJ CO-^ U1C N CO 050 i-iHOT^iOONCC'OO rr 

^ ' H HHHriWHHriHN N M W D N C(W C< ft « COCOCOCOlMCOlCOCOCO'^ WUUU}Sl(J 


52 


TRAVERSE TABLE 


25 Deg. 

253 Deg. 

25 h Deg. 

25f Deg. 

C 

H • 

CO 

c+ 

pj 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

•—< 
o 

p 

0.91 

0.42 

0.90 

0.43 

0.90 

0.43 

0.90 

0.43 

1 

1.81 

0.85 

1.81 

0.85 

1.81 

0.86 

1.80 

0.87 

2 

2.72 

1.27 

2.71 

1.28 

2.71 

1.29 

2.70 

1.30 

3 

3.63 

1.69 

3.62 

1.71 

3.61 

1.72 

3.60 

1.74 

4 

4.53 

2.11 

4.52 

2.13 

4.51 

2.15 

4.50 

2.17 

5 

5.44 

2.54 

5.43 

2.56 

5.42 

2.58 

5.40 

2.61 

6 

6.34 

2.96 

6.33 

2.99 

6.32 

3.01 

6.30 

3.04 

7 

. 7.25 

3.38 

7.24 

3.41 

7.22 

3.44 

7.21 

3.48 

8 

8.16 

3.80 

8.14 

3.84 

8.12 

3.87 

8.11 

3.91 

9 

9.06 

4.23 

9.04 

4.27 

9.03 

4.31 

9.01 

4.34 

10 

9.97 

4.65 

9.95 

4.69 

9.93 

4.74 

9.91 

4.78 

11 

10.88 

5.07 

10.85 

5.12 

10.83 

5.17 

10.81 

5.21 

12 

t 11.78 

5.49 

11.76 

5.55 

11.73 

5.60 

11.71 

5.65 

13 

12.69 

5.92 

12.66 

5.97 

12.64 

6.03 

12.61 

6.08 

34 

13.59 

6.34 

13.57 

6.40 

13.54 

6.46 

13.51 

6.52 

15 

14.50 

6.76 

14.47 

6.83 

14.44 

6.89 

14.41 

6.95 

16 

15.41 

7.18 

15.38 

7.25 

15.34 

7.32 

15.31 

7.39 

17 

16.31 

7.61 | 

16.28 

7.68 

16.25 

7.75 

16.21 

7.82 

18 

17.22 

8.03 

17.18 

8.10 

17.15 

8.18 

17.11 

8.25 

19 

18.13 

8.45 

18.09 

8.53 

18.05 

8.61 

18.01 

8.69 

20 

19.03 

S.87 

18.99 

8.96 

18.95 

9.04 

18.91 

9.12 

21 

19.94 

9.30 

19.90 

9.38 

19.86 

9.47 

19.82 

9.56 

22 

20.85 

9.72 

20.80 

9.81 

20.76 

9.90 

20.72 

9.99 

23 

21.75 

10.14 

21.71 

10.24 

21.66 

10.33 

21.62 

10.43 

24 

22.66 

10.57 

22.61 

10.66 

22.56 

10.76 

22.52 

10.86 

25 

23.56 

10.99 

23.52 

11.09 

23.47 

11.19 

23.42 

11.30 

26 

24.47 

11.41 

24.42 

11 .62 

24.37 

11.62 

24.32 

11.73 

27 

25.38 

11.83 

25.32 

11.94 

25.27 

12.05 

25.22 

12.16 

28 

26.28 

12.26 

26.23 

12.37 

26.17 

12 .4S 

26.12 

12.60 

29 

27.19 

12.68 

27.13 

12.80 

27.08 

12.92 

27.02 

13.03 

30 

28.10 

13.10 

28.04 

13.22 

27.98 

13.35 

27.92 

13.47 

31 

29.00 

13.52 

28.94 

13.65 

28.88 

13.78 

28.82 

13.90 

32 

29.91 

13.95 

29.85 

14.08 

29.79 

14.21 

29.72 

14.34 

33 

30.81 

14.37 

30.75 

14.50 

30.69 

14.64 

30.62 

14.77 

34 

31.72 

14.79 

31.66 

14.93 

31.59 

15.07 

31.52 

15.21 

35 

32.63 

15.21 

32.56 

15.36 

32.49 

15.50 

32.43 

15.64 

36 

33.53 

15.64 

33.46 

15.78 

33.40 

15.93 

33.33 

16.07 

37 

34.44 

16.06 

34.37 

16.21 

34.30 

16.36 

34.23 

16.51 

38 

35.35 

16.48 

35.27 

16.64 

35.20 

16.79 

35.13 

16.94 

39 

36.25 

16.90 

36.18 

17.06 

36.10 

17.22 

36.03 

17.38 

40 

37.16 

17.33 

37.08 

17.49 

37.01 

17.65 

36.93 

17.81 

41 

38.06 

17.75 

37.99 

17.92 

37.91 

18.08 

37.83 

18.25 

42 

38.97 

18.17 

38.89 

18.34 

38.81 

18.51 

38.73 

18.68 

43 

39.88 

18.60 

39.80 

18.77 

39.71 

18.94 

39.63 

19.12 

44 

40.78 

19.02 

40.70 

19.20 

40.62 

19.37 

40.53 

19.55 

45 

41.69 

19.44 

41.60 

19.62 

41.52 

19.80 

41.43 

19.98 

46 

42.60 

19.86 

42.51 

20.05 

42.42 

20.23 

42.33 

j 20.42 

47 

43.50 

20.29 

43.41 

20.48 

43.32 

20.66 

43.23 

20.85 

48 

44.41 

20.71 

44.32 

20.90 

44.23 

21.10 

44.13 

21.29 

49 

45.32 

21.13 

45.22 

21.33 

45.13 

21.53 

45.03 

21.72 

50 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

I 

Lat. 

Dep. 

Lat. 

6 

o 

G 

65 Deg. 

64£ 

Deg. 

64J Deg. 

64J Deg. 

CO 

■ H 

G 

i 







































































































TRAVERSE TABLE 


S3 


g 

5 

r* 

P 

25 Deg. 

25} Deg. 

25 £ Deg. 

25} Deg. 

C 

k— • 

c/j 

r* 

p 

O 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

o 

51 

46.22 

21.55 

46.13 

21.75 

46.03 

21.96 

45.94 

22.16 

51 

52 

47.13 

21.98 

47.03 

22.18 

46.93 

22.39 

46.84 

22.59 

52 

53 

48.03 

22.40 

47.94 

22.61 

47.84 

22.82 

47.74 

23.03 

53 

54 

48.94 

22.82 

48. S 4 

23.03 

48.74 

23.25 

48.64 

23.46 

54 

55 

49.85 

23.24 

49.74 

23.46 

49.64 

23.68 

49.54 

23.89 

55 

56 

50.75 

23.67 

50.65 

23.89 

50.54 

24.11 

50.44 

24.33 

56 

57 

51.66 

24.09 

51.55 

24.31 

51.45 

24.54 

51.34 

24.76 

57. 

58 

52.57 

24.51 

52.46 

24.74 

52.35 

24.97 

52.24 

25.20 

58 

59 

53.47 

24.93 

53.36 

25.17 

53.25 

25.40 

53.14 

25.63 

59 

60 

54.3S 

25.36 

54.27 

25.59 

54.16 

25.83 

54.04 

26.07 

60 

61 

55.28 

25.78 

55.17 

26.02 

55.06 

26.26 

54.94 

26.50 

61 

62 

56.19 

26.20 

56.08 

26.45 

55.96 

2-6.69 

55.84 

26.91 

62 

63 

57.10 

26.62 

56.98 

26.87 

56.86 

27.12 

36.74 

27 37 

C3 

64 

58.00 

27.05 

57.89 

27.30 

57.77 

27.55 

57.64 

27.80 

64 

65 

58.9 1 

27.47 

58.79 

27.73 

58.67 

27.98 

58.55 

28.24 

65 

66 

59.82 

27.89 

59.69 

28.15 

59.57 

28.41 

59.45 

28.67 

66 

67 

60.72 

28.321 

60.60 

28.58 

60.47 

28.84 

60.35 

29.11 

67 

68 

61.63 

28.74 

61.50 

29.01 

G1.38 

29.27 

61.25 

29.54 

63 

69 

62.54 

29.16 

62.41 

29.43 

62.28 

29.71 

62.15 

29.98 

09 

70 

63.44 

29.58 | 

63.31 

29.86 

63.18 

30.14 

63.05 

30.41 

70 

71 

64.35 

30.01 

64.22 

30.29 

64.08 

30.57 

63.95 

30.85 

71 

72 

65.25 

30.43 

65.12 

30.71 

64.99 

31.00 

64.85 

31 .28 

72 

73 

66.16 

30.85 

60.03 

31.14 

65.89 

31.43 

65.75 

31.71 

73 

74 

67.07 

31.27 

66.93 

31.57 

66.79 

31 .86 

66.65 

32.15 

74 

75 

67 ..97 

31.70 

67.83 

31.99 

67.69 

32.29 

67.55 

32.58 

75 

76 

68. SS 

32.12 

68.74 

32.42 

68.60 

32.72 

68.45 

33.02 

76 

77 

69.79 

32.54 

69.64 

32.85 

169.50 

33.15 

69.35 

33.45 

77 

78 

70.69 

32.96 

70.55 

33.27 j 

70.40 

33.58 

70.25 

33.89 

78 

79 

71.60 

33.39 

71.45 

33.70 i 

71 .30 

34.01 

71.16 

34.32 

79 

80 

72.50 

33.Si 

72.30 

34.13 ; 

72.21 

34.44 

72.06 

34.76 

80 

81 

73.41 

34.23 

73.26 

34.55 j 

73.11 

34.87 

72.96 

35.19 

81 

82 

74.32 

34.65 

74.17 

34.98 i 

74.01 

35.30 

73.86 

35.62 

82 

83 

75.22 

35.08 

75.07 

35.41 

74.91 

35.73 

74.76 

36.06 

83 

84 

76.13 

35.50 

75.97 

35.83 i 

75.82 

30.16 

75.66 

36.49 

84 

85 

77.04 

35.92 

76.88 

36.26 1 

76.72 

36.59 

76.56 

36.93 

85 

86 

77.94 

36.35 

77.78 

36.68 

77.62 

37.02 

77.46 

37.36 

86 

87 

78.85 

36.77 

78.69 

37.11 

78.52 

37.45 

78.36 

37.80 

87 

88 

79.76 

37.19 

79.59 

37.54 

79.43 

37.88 

79.26 

33.23 

88 

89 

80.66 

37.61 

80.50 

37.90 

SO. 33 

38.32 

80.16 

38.67 

89 

90 

81.57 

38.04 

81.40 

38.39 

81.23 

38.75 

81.06 

39.10 

90 

91 

82.47 

38.46 

82.31 

38.82 

82.14 

39.18 

81.96' 

39.53 

91 

92 

83.38 

38.88 

83.21 

39.24 

83.04 

39.61 

82.86 

39.97 

92 

93 

84.29 

39.30 

84.11 

39.67 

83.94 

40.04 

83.76 

40.40 

93 

94 

85.19 

39.73 

85.02 

40.10 

84.84 

40.47 

84.67 

40.84 

94 

95 

86. 10 

40.15 

85.92 

40.52 

85.75 

40.90 

85.57 

41 .27 

95 

96 

87.01 

40.57 

86.83 

40.95 

86.65 

41.33 

86.47 

41.71 

96 

- 97 

87.91 

40.99 

87.73 

41.38 

!87.55 

41.76 

87.37 

42.14 

97 

98 

88.82 

41.42 

88.64 

41.80 

88.45 

42.19 

88.27 

42.58 

98 

99 

89.72 

41.84 

89.54 

42.23 

89.36 

42.62 

89.17 

43.01 

09 

100 

90.63 

42.26 

90.45 

42.66 

90.26 

43.05 

90.07 

43.44 

100 

6 

V 

r- 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

rJ 

Vi 

6 

J 

65 Deg. 

64} Deg. 

C4\ Deg. 

i 

64} Deg. 

c a 

SS 
* - 






























































































54 


TRAVERSE TARLE. 


0 

S i 

P 1 

26 Deg. 

26 \ Deg. 

26^ Deg. 

26} Dag. 

c 

35* 

<“* 

p 

3 

vD 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. | 

Dep. 

D 

o 

o 

1 

0.90 

0 44 

0.90 

0.44 

0.89 j 

0.45 

0.89 

0.4 5 | 

1 

2 

1.80 

0.83 

1.79 

0.8S 

1.79 

0.89 

1.79 

0 90 | 

2 

3 

2.70 

1.32 

2.69 

1.33 

2.08 

1.34 

2.63 

1 .35 

3 

4 ! 

3.00 

1.75 

3.59 

1.77 

3 . 58 

1 .78 

3.57 

1.80 ' 

4 

5 1 

4.4.9 

2.19 

4.48 

2.21 

4.47 

2.23 

4.40 

O ‘>% 

• /*•/ 

5 

6 1 

5.39 

2.63 

5.33 

2,65 

5.37 

2 . 63 

5.30 

2 . 70 

0 

7 I 

0.29 

3.07 

0.28 

3.10 | 

6.26 

3.12 

0.25 

3. 15 

7 

8 

7.19 

3.51 

7.17 

3.51 J 

7. 16 

3 . 57 

7.14 

3.60 

8 

9 

8.09 

3.95 

8.07 

3.93 i 

8.05 

4.02 

8.01 

4.05 

9 

10 

8.99 

4.33 

8.97 

4.42 

8.95 

4.40 

8.93 

4.5) 

10 

11 

9.89 

4.32 

9.87 

4.87 1 

9.34 

4.91 

9.82 

4.9 > 

11 

12 

10.79 

5.26 

10.76 

5.31 

10.74 

5.35 

10.72 

5.40 

12 

13 

11 .6.8 

5.70 

11.66 

5.75 

11.63 

5.80 

11.61 

5.83 

13 

14 

12.58 

6.14 

12.50 

6. 19 

12.53 

6.25 

12.50 

6.30 

14 

15 

13.48 

6.58 

13.45 

6.03 

13.42 

6.09 

13.39 

6.75 

i5 

10 

14.38 

7.01 

14.35 

7.08 

14.32 

7.14 

14.29 

7.20 

10 

17 

15.28 

7.45 

15.25 

7.52 

15.21 

7.59 

15. 13 

7.65 

17 

IS 

10.18 

7.89 1 

16.14 

7.96 

16. 1 l 

8.03 

16.07 

8.10 

18 

19 

17.03 

8.33 

17.04 

8.40 

17.00 

8.48 

16.97 

8.55 

19 

20 

17.93 

8.77 

17.94 

8.85 

17.90 

8.92 

17.86 

9. CO 

20 

21 

18.87 

9.21 

18.83 

9.29 

13.79 

9.37 j 

18.75 

9.45 

21 

22 

19.77 

9.64 

19.73 

9.73 

19.09 

9.82 i 

19.65 

9.90 

oo 

A* A# 

• 23 

20.67 

10.08 

20.03 

10.17 

20.58 

10.20 

20.54 

10.35 

23 

24 

21.57 

10.52 

2 1 .52 

10.011 

21.48 

10.71 

21 .43 

10.80 

24 

25 

22.47 

10.96 

22.42 

11.00 

22.37 

11.15 

! r>.> 

1 1.25 

25 

20 

23.37 

11.40 

23.32 

11.50 ! 

23.27 

11.60 

|23.22 

11.70 

20 

27 

24.27 

1 1.84 

24.22 

ii. 94 ; 

24.16 

12.05 

I 24.11 

12.15 

27 

28 

25.17 

12.27 

25 . 1 l 

12.38 

25.00 

12.49 

1 25.09 

12.60 

23 

29 

23.03 

12.71 

20.01 

12.83 

25.95 

12.94 

25.90 

13.05 

29 

30 

20.90 

13.15 

20.91 

13.27 

20.85 

13.39 

| 20.79 

13.50 

3!) 

31 

27.86 

13.59 

27.80 

13.71 

27.74 

13.83 

127.08 

13.95 

31 

32 

23.70 

14.03 

23.70 

14.15 

23.64 

14.28 

1 23.53 

14.40 

32 

33 

29.00 

14.47 

29.09 

14.0!) 

29.53 

14.72 

j 29.47 

! 14.85 

33 

34 

30.50 

14.90 

30.49 

15.04 

30.43 

15. 17 

| 30.36 

15.30 

34 

35 

31.40 

15.34 

31.39 

15.43 

31.32 

15.62 

31.25 

15.75 

35 

30 

32.39 

15.78 

32.29 

15.92 

32.22 

10.00 

!32.15 

1 0.20 

30 

37 

33 • 20 

18.22 

33.13 

10.35 

33.11 

10.51 

j 33.04 

1 6.05 

37 

33 

31.15 

16.66 

34.03 

10.81 

34.0 l 

10.90 

j 33.93 

17.10 

38 

39 

35.05 

,17.10 

34.93 

17.25 

34.90 

17.40 

134.83 

17.55 

39 

40 

35.95 

i 17.53 

35.87 

17.69 

35.80 

17.85 

35.72 

18.00 

40 

41 

30.85 

17.97 

30.77 

18.13 

30.09 

18.29 

30.61 

IS. 45 

41 

42 

37.75 

13 .41 

37.07 

18.53 

37.59 

18.74 

37.51 

IS. 90 

42 

43 

33.65 

1 18.85 

33.57 

19.02 

33.48 

19.19 

33.40 

19.35 

43 

44 

I 39.55 

19.29 

39.46 

19.40 

39.33 

19.03 

39.29 

19.80 

44 

45 

40.45 

119.73 

40.30 

19.90 

40.27 

20.08 

40. IS 

I 20.25 

45 

40 

41.34 

|20.17 

41.20 

20 . 35 

41.17 

20 . 53 

41.03 

20 . 70 

40 

47 

42.24 

20.60 

42. ! 5 

20.79 

42.00 

20.97 

41.97 

21.15 

47 

48 

43.14 

21.04 

43.05 

21.23 

42.96 

21.42 

42.80 

1 21.00 

48 

49 

44.04 

21.48 

43.95 

21.67 

43.85 

21.80 

43.70 

| 22.05 

49 

60 

44 .94 

| 21.92 

44.84 

22.11 

44.75 

22.31 

44.65 

! 22 . 50 

50 

© 

V 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

I-m! t. 

• 

© 

o 

c 

cd 

+-3 

CO 
• —1 

Q 

64 Dog. 

63} Deg. 

1 

63 Deg. 

— o 

63} Deg. 

5 

i 




































































































































TRAVERSE TABLE 


55 


• 

w 

r*» 

P 

26 Deg. 

26} Deg. 

261 

Deg. 

2 6* 

Deg. 

o 

• 

a j 

r-+ 

o 

p 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

ss 

o 

p 

51 

45.84 

22.36 1 

45.74 

22.56 

45.64 

22.76 

46 51 

22.90 

51 

52 

46.74 

22.80 

46.64 

23.00 

46.54 

23.20 

40.43 

23.41 

52 

52 

47.64 

23.23 

47.53 

23.44 

47.43 

23.65 

47.33 

23.83 

53 

54 

48.53 

23.67 

48.43 

23.88 

48.33 

24.09 

48 22 

24.31 

54 

55 

49.43 

24.11 

49.33 

24.33 

49.22 

24.54 

49.11 

21.76 

55 

p <■» 

O’) 

59.33 

24.55 

50.22 

24.77 

50.12 

24.09 

50.01 

25.21 

56 

57 

51 .23 

21.99 

51.12 

25.21 

51.01 

25.43 

50.90 

25.66 

57 

53 

52. 13 

25.43 

52.02 

25.65 

51.91 

25 88 

51.79 

26.1 1 

58 

59 

53.03 

25.86 

52.92 

26.09 

52.80 

26.33 

52.69 

26.56 

59 

69 

53.93 

26.30 

53.8 1 

26.54 

53.70 

26 77 

53.58 

27.01 

GO 

61 

51.83 

26.74 

54.71 

26.93 

54.59 

27.22 

54.47 

27.46 

61 

62 

55.73 

27. 18 

55.61 

27.42 

55.49 

27.66 

55.36 

27.91 

62 

69 

55.62 

27.62 

56.50 

27.86 

55.33 

23.11 

58.26 

28.36 

63 

61 

57.52 

2*.06 

57.40 

28.31 

57.28 

28.56 

57.15 

28.81 

64 

65 

53.42 

23.49 

58.30 

28.75 

58.17 

29.00 

58.04 

29.26 

65 

65 

59.32 

28.93 

59.19 

29.19 

59.07 

29.45 

58.94 

29.71 

66 

67 

60.22 

29.37 

60.09 

29.63 

59.96 

29.90 

59.83 

39. 16 

67 

65 

61.12 

29.81 

60.99 

3J.03 

60.86 

39.34 

60.72 

30.61 

63 

CU 

62.02 

30.25 

61.88 

30.52 

61.75 

39.79 

61.62 

31.06 

69 

70 

62.92 

39.69 

62.78 

30.93 

62.65 

31.23 

62.51 

31.51 

70 

71 

63.81 

31.12 

63.68 

31.40 

63.54 

31.08 

63.40 

31.96 

71 

72 

64.71 

31 .56 

61.57 

31.84 

64.44 

32.13 

64.29 

32.41 

72 

72 

65.61 

32.00 

65.47 

32.29 

65.33 

32.57 

65.19 

32.86 

73 

74 

66 .5 1 

32.44 

66.37 

32.73 

66.23 

33.02 

66.08 

33.31 

74 

75 

67.41 

32.88 

67.27 

33.17 

67.12 

33.46 

68.97 

33.76 

75 

76 

63.31 

33.32 

68.16 

69.06 

33.61 

68.01 

33.9 L 

67.87 

34.21 

76 

77 

69.21 

33.75 

31.06 

68.91 

31.38 

68.76 

34.66 

77 

78 

70.1 l 

34.19 

69.96 

31.50 

69.80 

31.89 

69.65 

35.11 

78 

79 

71.00 

31.63 

70.85 

34.94 

70.70 

35.25 

70.55 

35.56 

79 

89 

71.90 

35.07 

71.75 

35.33 

71 .59 

35.70 

71.44 

38.01 

80 

81 

72.80 

35.51 

72.65 

35.83 

72.19 

38.14 

72.33 

36.46 

81 

82 

73.70 

35.95 

73.54 

35.27 

73.38 

36.59 

73.22 

36.91 

82 

82 

7 1.60 

36.38 

74.44 

36.71 

74.28 

37.03 

74. 12 

37.38 

83 

81 

75.50 

36.82 

75.34 

37. 15 

75.17 

37.48 

75.01 

37.81 

84 

85 

76.40 

37.26 

76. *3 

37.59 

76.07 

37.93 

75.90 

38.26 

85 

85 

77.33 

37.70 

77. 13 

33.04 

76.96 

38.37 

70.80 

38.71 

86 

87 

78.20 

38.14 

78.03 

33.48 

77.86 

38.82 

77.69 

39.16 

87 

88 

79.0“ 

38.58 

78.92 

33.92 

7S. 75 

39.27 

78.58 

39.61 

88 

89 

79.99 

39.01 

79.82 

39.36 

79.65 

39.71 

79.48 

49.06 

89 

90 

80.39 

39.45 

80.72 

39.81 

SO. 54 

40.16 

80.37 

40.51 

90 

91 

81.79 

39.89 

81.62 

40.25 

81 .44 

40.60 | 

81.28 

40.98 

91 

92 

82.69 

40.33 

82.51 

40.69 

82.33 

41.05 

82.15 

41.41 

92 

92 

83.59 

40.77 

83.41 

41.13 

83.23 

41.50 | 

83.05 

41.86 

93 

91 

8 1.49 

41.21 

84.31 

41.58 

84.12 

41.94 

83.94 

42.31 

94 

95 

85.39 

41.65 

85.20 

42.02 

85.02 

42.39 

84.83 

42.76 

95 

96 

86.23 

42.03 

86.10 

42.46 

85.91 

42.83 

85.73 

43.21 

96 

97 

87.18 

42.52 

87.00 

42.90 

86.81 

43.28 

86.62 

43.66 

97 

93 

83.03 

42.95 

87.89 

43.34 

87.70 

43.73 

87.51 

44.11 

93 

99 

88.93 

43.40 

88.79 

43.79 

88.60 

44.17 

83.40 

44.56 

99 

109 

89.88 

43.84 

89.69 

44.23 

89.49 

44.62 

89.30 

45.01 

100 j 

6 

o 

c 

Dcp. 

Lat, 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o' f 
a 3 

ci 

73 

3 

G4 Deg. 

63} Deg. 

63} Deg. ; 

63} Deg. 

Cw | 

♦J 

ec fc 

Q ' 
} 







































































































66 


TRAVERSE TABLE 


a 

r-t- 

ps 

27 Deg. 

27} Deg. 

27} 

Deg. 

27} 

Deg. 

g 

U) 

c~* 

P 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

D 

o 

p 

l 

0.89 

0.45 

0.89 

0.46 

0.89 

0.46 

0.88 

0.47 

i 

2 

1.78 

0.91 

1.78 

0.92 

1 .77 

0.92 | 

1.77 

0.93 

2 

3 

2.67 

1.36 

2.67 

1.37 

2.66 

1.391 

2.65 

1.40 

3 

4 

3.56 

1.82 

3.56 

1.83 

3.55 

1.85 

3.54 

1.86 

4 

5 

4.45 

2.27 

4.45 

2.29 

4.44 

2.31 

4.42 

2.33 

5 

6 

5.35 

2.72 

5.33 

2.75 

5.32 

2.77 

5.31 

2 .79 

6 

7 

6.24 

3.18 

6.22 

3.21 

6.21 

3.23 

6.19 

3.26 

7 

8 

7.13 

3.63 

7.11 

3.66 

7.10 

3.69 

7.08 

3.72 

8 

9 

8.02 

4.09 

8.00 

4.12 

7.98 

4.16 

7.96 

4.19 

9 

10 

8.91 

4.54 

8.89 

4.58 

8.87 

4.62 

8.85 

4.66 

10 

11 

9.80 

4.99 

9.78 

5.04 

9.76 

5.08 

9.73 

5.12 

11 

12 

10.69 

5.45 

10.67 

5.49 

10.64 

5.54 

10.62 

5.59 

12 

13 

11.58 

5.90 

11.56 

5.95 

11.53 

6.00 I 

11.50 

6.05 

13 

14 

12.47 

6.36 

12.45 

6.41 

12.42 

6.46 

12.39 

6.52 

14 

15 

13.37 

6.81 

13.34 

6.87 

13.31 

6.93 

13.27 

6.98 

15 

10 

14.26 

7.26 

14.22 

7.33 

14.19 

7.39 

14.16 

7.45 

16 

17 

15.15 

7.72 

15.11 

7.78 

15.08 

7.85 

15.04 

7.92 

17 

18 

16.04 

8.17 

16.00 

8.24 

15.97 

8.31 

15.93 

8.38 

18 

19 

16.93 

8.63 

19.89 

8.70 

16.85 

8.77 

16.81 

8.85 

19 

20 

17.82 

9.08 

17.78 

9.16 

17.74 

9.23 

17.70 

9.31 

20 

21 

18.71 

9.53 

18.67 

9.62 

18.63 

9.70 

18.58 

9.78 

21 

22 

19.60 

9.99 

19.56 

10.07 

19.51 

10.16 

19.47 

10.24 

9‘2 

23 

20.49 

10.44 

20.45 

10.53 

20.10 

10.62 

20.35 

10.71 

23 

24 

21.38 

10.90 

21 .34 

10.99 

21.29 

11.08 

21.24 

11.17 

24 

25 

22.28 

11.35 

22.23 

11.45 I 

22.18 

11.54 

22.12 

11 .64 

25 

26 

23.17 

11.80 

23.11 

11.90 

23.06 

12.01 

23.01 

12.11 

26 

27 

24.06 

12.26 

24.00 

12.30 I 

23.95 

12.47 

23.89 

12.57 

27 

28 

24.95 

12.71 

24.89 

12.82 

24.84 

12.93 

24.78 

13.04 

28 

29 

25.84 

13.17 

25.78 

13.28 

25.72 

13.39 

25.66 

13.50 

29 

30 

26.73 

13.62 

26.67 

13.74 

26.61 

13.85 

26.55 

13.97 

30 

31 

27.62 

14.07 

27.56 

14.19 

27.50 

14.31 

27.43 

14.43 

31 

32 

28.51 

14.53 

28.45 

14.65 

28.38 

14.78 

28.32 

14.90 

32 

33 

29.40 

14.98 

29.34 

15.11 

29.27 

15.24 

29.20 

15.37 

33 

34 

30.29 

15.44 

30.23 

15.57 

30.16 

15.70 

30.09 

15. S3 

34 

35 

31.19 

15.89 

31.12 

16.03 

31.05 

16.16 

30.97 

16.30 

35 

36 

32.08 

16.34 

32.00 

16.48 

31.93 

16.62 

31.86 

16.76 

36 

37 

32.97 

16.80 

32.89 

16.94 

32.82 

17.08 

32.74 

17.23 

37 

38 

33.80 

17.25 

33.78 

17.40 

33.71 

17.55 

33.63 

17.69 

38 

39 

34.75 

17.71 

34.07 

17.86 

34.59 

18.01 

34.51 

18.16 

39 

40 

35.64 

18.16 

35.56 

18.31 

35.48 

18.47 

35.40 

18.62 

40 

41 

36.53 

18.61 

36.45 

18.77 

36.37 

18.93 

36.28 

19.09 

41 

42 

37.42 

19.07 

37.34 

19.23 

37.25 

19.39 

37.17 

19.56 

42 

43 

38.31 

19.52 

38.23 

19.69 

38.14 

19.86 

38.05 

20.02 

43 

44 

39.20 

19.98 

i 39.12 

20.15 

39.03 

20.32 

38.94 

20.49 

44 

45 

40.10 

20.43 

1 40.01 

20.60 

39.92 

20.78 

39.82 

20.95 

45 

46 

40.99 

20.88 

40.89 

21.06 

40.80 

21.24 

40.71 

21.42 

46 

47 

41.88 

21.34 

41.78 

21.52 

41.69 

21.70 

41.59 

21.88 

47 

48 

42.77 

21.79 

l42.67 

21.98 

42.58 

22.16 

42.48 

22.35 

48 

49 

43.66 

22.25 

i 43.56 

22.44 

43.46 

22.63 

43.36 

22.82 

49 

50 

44.55 

22.70 

44.45 

22.89 

44.35 

23.09 

44.25 

23.28 

50 

6 

o 

G 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

V 

c 

73 

5 

63 Deg. 

62} Deg. 

1 

6 Qi 

2 

Deg. 

62} Deg. 

t/2 

Q 
































































































TRAVERSE TARLE. 


57 


I 

o ! 
►— • 

c— 

27 Deg. 

27£ Deg. 

071 

® i) 

Deg. 

271 Deg. 

Distance. 

O 

o 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lcit* 

Dep. 

Lat. 

Deo. 

A 

J 51 

45.44 

23.15 

45.34 

23.35 

45.24 

23.55 

45.13 

23.75 

51 

! 52 

46.33 

23.61 

46.23 

23.81 

48.12 

24.01 

46.02 

24.21 

52 

j 53 

47.22 

24.06 

47.12 

24.27 

47.01 

24.47 

46.00 

24.63 

53 

51 

48.11 

24.52 

48.01 

24.73 

47.90 

24.93 

47.79 

25.14 

54 

55 

49.01 

24.97 

48.90 

25.18 

48.79 

25.40 

48.67 

25.61 

55 

50 

49.90 

25.42 

49.78 

25.64 

49.67 

25.86 | 

49.56 

26.07 

50 

5? 

50.79 

25.88 

50.67 

26.10 

50.56 

26.32 

50.44 

26.54 

57 

58 

51.68 

26.33 

51.58 

26.56 

51.45 

26.78 

51.33 

27.01 

58 

59 

52.57 

26.79 

52.45 

27.01! 

52.33 

27.24 

52.21 

27.47 

59 

6 U 

53.46 

27.24 

53.34 

27.47 

53.22 

27.70 

53.10 

27.94 

60 

61 

54.35 

27.69 

54.23 

27.93 | 

54.11 

23.17, 

53.98 

23.40 

61 

62 

55.24 

28.15 

55.12 

28.39 j 

54.99 

28.63 

54.87 

28.87 

62 

63 

56.13 

28.60 

! 56.01 

28.85 

55.88 

29.09 

55.75 

29.33 

63 

64 

57.02 

29.06 

56.90 

29.30 1 

56.77 

29.55 1 

56.64 

29.80 

64 

65 

57 92 

29.51 

57.79 

29.76 

57.66 

30.01 ! 

57.52 

30.26 

65 

66 

58.81 

29.96 

58.68 

30.22 

58.54 

30.48 

58.41 

30.73 

66 

67 

59.70 

30.42 

59.56 

30.68 

1 59.43 

30.94 j 

59.29 

31.20 

67 

68 

60.59 

30.87 

60.45 

31.14 

60.32 

31 .40 

60.18 

31.66 

68 

69 

61.48 

31.33 

61.34 

31.59 

61.20 

31 .86 

61.06 

32.13 

69 

70 

62.37 

31.78 

62.23 

32.05 

62.09 

32.32 j 

61.95 

32.59 

70 

71 

63.26 

32.23 

69.12 

32.51 

62.98 

32.78 i 

62.83 

33.06 

71 

72 

64.15 

32.69 

64.01 

32.97 

63.86 

33.25 I 

63.72 

33.52 

72 

73 

65.1)4 

33.14 

64.90 

33.42 

64.75 

33.71 | 

64.69 

33.99 

73 

74 

65.93 

33.60 

65.79 

33.88 

65.64 

34.17, 

65.49 

34.40 

74 

75 

06.83 

34.05 

66.68 

34.34 

66.53 

34.63 

66.37 

34.92 

75 

76 

07.72 

34.50 

67.57 

34.80 

67.41 

35.09 

35.55 

67.20 

35.39 

76 

77 

68.61 

34.96 

68.45 

35.26 

68.30 

68.14 

35.85 

77 

78 

09.50 

35.41 

69.34 

35.71 

69.19 

36.02 

69.03 

36.32 

7% 

79 

70.39 

35.87 

70.23 

36.17 

70.07 

36.48 

69.91 

36.78 

7tf 

80 

71.28 

36.32 

71.12 

36.63 

. 

70.96 

36.94 

70.80 

37.25 

80 

81 

72.17 

36.77 

72.01 

37.09 

71.85 

37.40 

71.63, 

37.71 

81 

82 

73.06 

37.23 

72.90 

37.55 

72.73 

37.86 

72.57 

38.18 

82 

83 

73.95 

37.68 

73.79 

38.00 

73.62 

33.33 

73.45 

38.65 

83 

84 

74.84 

33.14 

74.68 

38.46 

74.51 

38.79 

74.34 

39.11 

84 

85 

75.74 

38.59 

75.57 

33.92 

75.40 

39.25 

75.22 

39.58 

85 

86 

76.63 

39.04 

76.46 

39.38 

76.28 

39.71 

76.11 

40.04 

86 

87 

77.52 

39.50 

77.34 

39.83 

77.17 

40.17 

70.99 

40.51 

87 

88 

78.41 

39.95 

78.23 

40.29 

i78.06 

40.63 

77.88 

40.97 

88 

89 

79.30 

40.41 

79.12 

40.75 

78.94 

41.10 

78.76 

41:44 

89 

90 

80.19 

40.86 

8 - 0.01 

41.21 

79.83 

4i .56 

79.65 

41.91 

90 

91 

81.08 

41.31 

80.90 

41.67 

80.72 

42.02 

:80.53 

42.37 

91 

92 

81 97 

41.77 

81.79 

42.12 

81.60 

42.48 

|81.42 

42.84 

92 

93 

82.86 

42.22 

82.68 

42.58 

82.49 

42.94 

82.30 

43.30 

93 

94 

83.75 

42.68 

83.57 

43.04 

83.38 

43.40 

83.19 

43.77 

94 


84.65 

43.13 

84.46 

43.50 

84.27 

43.87 

84.07 

44.23 

95 

96 

85.54 

43.58 

85.35 

43.96 

85.15 

44.33 

84.96 

44.70 

96 

97 

86.43 

44.04 j 

86.23 

44.41 

86.04 

44.79 

85.84 

45.16 

97 

98 

87.32 

44.49 

87.12 

44.87 

86.93 

45.25 

86.73 

45.63 

98 

99 

88.21 

44.95 

88.01 

45.33 

87.81 

45.71 

87.61 

46.10 

99 

100 

89.10 

45.40 

88.90 

45.79 

88.70 

46.17 

88.50 

46.56 

100 

6 ; 
o 

a ! 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

'1 

Dep. 

Lat. 

8 S 
s \ 

rf 

«-> 

M 

X 

-i ! 
) 

63 Deg. 

G2| Deg. 

62.L 

Dog. : 

l 

62 ; 

Deg. 

5 J 

. Z‘ t 

' i 
























































































































58 


TRAVERSE TAELE 


o 

c r/ 

<-+• 

P 

28 Deg. 

28} Deg. 


Deg. 

28} Deg. 

o! 

05 j 

P [ 

3 

a 

o 

I .jilt. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

! ^ep. 

2 

O 

» 

1 

0.88 

0.47 

0.88 

0.47 

0.88 

0.48 

0.88 

0.48 

1 

2 

1.77 

0.94 

1.76 

0.95 

1.76 

0.95 

1 .75 

0.96 

2 

3 

2.65 

1.41 

2.64 

1.42 

2.64 

1.43 

2.63 

1 .44 

3 

4 

3.53 

1.88 

3.52 

1.89 

3.52 

1.91 

3.51 

1.92 

4 

5 

4.41 

2.35 

4.40 

2.37 

4.39 

2.39 

4.38 

2.40 

5 

G 

5.30 

2.82 

5 . 29 

2.84 

5.27 

2.86 

5.26 

2.89 

6 

7 

G. 18 

3.29 

6.17 

3.31 

6 . 15 

3.34 

6.14 

3.37 

7 

8 

7.0G 

3.76 

7.05 

3.79 

7.03 

3.82 

7.01 

3.85 

8 

9 

7.95 

4.23 

7.93 

4.26 

7.91 

4.29 

7.89 

4.33 

9 

10 

8.83 

4.69 

8.81 

4.73 

8 .79 

4.77 

8.77 

4.81 

10 

11 

9.71 

5.16 

9.69 

5.21 

9.67 

5.25 

9.64 

5.29 

11 

12 

10. GO 

5.63 

10.57 

5.68 

10.55 

5.73 

10.52 

5.77 

12 

13 

11.48 

6.10 

11.45 

6.15 

11.42 

6.20 

11.40 

G. 25 

13 

14 

12 . 36 

6.57 

12.33 

6.G3 

12.30 

6.68 

12.27 

6.73 

14 

15 

13.24 

7.04 

13.21 

7.10 

13.18 

7.16 

13.15 

7.2! 

15 

16 

14. 13 

7.51 

14.09 

7.57 

14.06 

7.63 

14.03 

7.70, 

16 

17 

15.01 

7.98 

14.98 

8.05 

14.94 

8.11 ! 

14.90 

8.18 

17 

18 

15.89 

8.45 

15.86 

8.52 

15.82 

8.59 

15.78 

8.66 

18 

19 

16.78 

8.92 

1G.74 

8.99 

16.70 

9.07 

16.66 

9.14 

19 

20 

17.GG 

9.39 

17.62 

9.47 1 

17.58 

9.54 

17.53 

9.62 

20 

21 

18.54 

9.86 

18.50 

9.94 | 

18.46 

10.02 

18.41 

10.10 

21 

90 

19.42 

10.33 

19.38 

10.41 

19.33 

10.50 

19.29 

10.58 

22 

23 

20.31 

10.80 

20.26 

10.89 

20.21 

10.97 

20.16 

11 .06 

23 

24 

21.19 

11.27 

•21.14 

11.36 

21.09 

11.45 

21.04 

11 .54 

24 

25 

22.07 

11.74 

,22.02 

11.83 

21.97 

11.93 

21 .92 

12.02 

25 

26 

2 2.9G 

12.21 

i 22.90 

12.31 

22.85 

12.41 ! 

22.79 

12.51 

26 

27 

23.84 

12.68 

' 23.78 

12.78 

23.73 

12.88 i 

23.67 

12.99 

27 

28 

24.72 

13.15 

24.66 

13.25 

24.61 

13.36 j 

24.55 

13.47 

28 

29 

25.61 

13.61 

25.55 

13.73 

25.49 

13.84 

25.43 

13.95 

29 

30 

2G.49 

14.08 

2G.43 

14.20 

26.36 

14.31 | 

26.30 

14.43 

30 

31 

27.37 

14.55 

27.31 

14.67 

27.24 

14.79 I 

27.18 

14.91 

31 

32 

28.25 

15.02 

28.19 

15. 15 

28. 12 

15.27 ! 

28.06 

15.39 

32 

33 

29.14 

15.49 

29.07 

15.62 

29.00 

15.75 

28.93 

15.87 

33 

34 

30.02 

15.96 

29.95 

16.09 

29.88 

16.22 

29.81 

16.35 

34 

35 

30.90 

16.43 

30.83 

16.57 

30.76 

16.70 

30.69 

16 83 

35 

3G 

31.79 

16.90 

31.71 

17.04 

31.64 

17.18 

31.56 

17.32 

36 

37 

32.67 

17.37 

32.59 

17.51 

32. >2 

17.65 

32.44 

17.80 

37 

38 

33.55 

17.84 

33.47 

17.99 

33.39 

18.13 

33.32 

18.28 

38 

39 

34.43 

18.31 

! 34.35 

18.46 

34.27 

18.61 

34.19 

18.76 

39 

40 

35.32 

18.78 

j 35.24 

18.93 

35.15 

19.09 

35.07 

19.24 

40 

41 

30.20 

19.25 

36.12 

19.41 

36.0-3 

19.56 

35.95 

19.72 

41 

42 

37.08 

19.72 

j 37.00 

19.88 

!36.91 

20.04 

36.82 

20.20 

42 

43 

37.97 

20.19 

37.88 

20.35 

37.79 

20.52 

i 37.70 

20.68 

43 

44 

38.95 

20.66 

38.76 

20.83 

38.67 

20.99 

S 38.58 

21.16 

44 

45 

39.7-3 

21.13 

39.64 

21.30 

39.55 

21.47 

39.45 

21.64 

45 

4G 

40.62 

21.60 

40.52 

21.77 

40.43 

21.95 

40.33 

22.13 

4 - 

47 

41.50 

22.07 

41.40 

22.25 

41.30 

22.43 

41.21 

22.61 

47 

48 

42.38 

22.53 

42.28 

22.72 

42.18 

22.90 

42.08 

23.09 

48 

49 

43.26 

23.00 

43.16 

23.19 

43.06 

23.38 

42.96 

23.57 

49 

50 

44.15 

23.47 

44.04 

23.67 

43.94 

23.86 

43.84 

24.05 

50 

rice. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

! ♦-» 
i i 

d 

rj 

zr. 

tfl 

5 

02 Deg. 

61 1 Deg. 

fil* 

Deg. 

1 

61} Deg. 

j 

ci 

■4-i 

5 






























































































TRAVERSE TAIiLK. 


50 


Distance. 

23 Deg. 

Deg. 

i 

2Deg. 

28| Deg. 

c 

Th * 

Lat. j 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

C5 

51 

45.03 | 

23.94 

44.93 | 

24.14 

44.82 

24.34 

44.71 

24.53 

51 

52 

45.91 

24.41 ! 

45.81 j 

24.01| 

45.70 

24.81 | 

45.59 

25.01 

52 

50 

40.80 ! 

24.88 

40.09 

25.09 

46.58 

25.29 

46.47 

25.49 

53 

54 ; 

47.63 I 

25.35 

47.57 

25.56 i 

47.40 

25.77 

47.34 

25.97 

54 

55 

48.56j 

25.82 

48.45 

20.03 

48.33 

26.24 

48.22 

20.45 

55 

50 

49.45 

20.29 

49.33 

20.51 

49.21 

26.72 

49.10 

26.94 

56 

57 

50.33 

20.70 ! 

50.21 

20.98 

50.09 

27.20 

49.97 

27.42 

57 

58 

51.21 | 

27.23 

51.09 

27.45 

50.97 

27.68 

50.85 

27.90 

58 

59 

52.09 | 

27.70 

51.97 

27.93 

51.85 

28.15 

51 .73 

23.38 

59 

00 

52.93 | 

28.17 | 

52.85 | 

28.40 

52.73 

28.63 

52.60 

28.80 

60 

01 

53.80 

28.64j 

53.73 

28.87 

53.01 

29.11 

53.48 

29.34 

61 

02 

54.74 

29.11 

54.02 

29.35 

54.49 

29.58 

54.30 

29.82 

62 

00 

55.03 

29.58 

55.50 

29.82 

55.37 

30.06 

55.23 

30.30 

63 

04 

50.51 

30.05 i 

50.38 

30.29 

50.24 

30.54 

50.11 

30.73 

64 

05 

57.39 

30.52 ' 

57.26 

30.77 

57.12 

31.02 

50.99 

31.20 

65 

60 

58.27 

30.99 : 

58. 14 

3 l. 24 

i58.00 

31.49 

57.80 

31.75 

GK 

07 

59. 1 0 

31.45 

59.02 

31.71 

58.88 

31.97 

58.74 

32.23 

07 

68 

00.04 

31 .92 

59.90 

32.19 

59.76 

32.45 

59.02 

32.71 

63 

69 

00.92 

32.39 

00.78 

32.60 

60.04 

32.92 

60.49 

33.19 

69 

70 

01 .SI 

32.86 

61.00 

33.13 

01.52 

33.40 

61.37 

33.07 

70 

71 

02.69 

33.33 

02.54 

33.6 1 

02.40 

33.88 

62.25 

34.15 

71 

72 

63.57 

33.80 

63.42 

34.08 

63.27 

34.30 

63. 12 

34.03 

72 

73 

64.40 

34.27 

04.30 

34.55 

64.15 

34.83 

64.00 

35. 1 l 

73 

74 

65.34 

34.74 

05. 19 

35.03 

05.03 

35.31 

64.83 

35.59 

74 

75 

00.22 

35.21 

1 60.07 

35.50 

65.91 

35.79 

05.75 

36.07 

75 

70 

07.10 

35.08 

06.95 

35.97 

66.79 

36.26 

!66.63 

36.50 

70 

77 

67.99 

36.15 

67.83 

36.45 

67.67 

36.74 

67.51 

37.04 

77 

78 

68.87 

36.62 

08.71 

36.92 

68 .55 

37.22 

68.38 

37.52 

78 

79 

69.75 

37.09 

69.59 

37.39 

69.43 

37.70 

!69.26 

3$. 00 

79 

80 

70.04 

37.56 

70.47 

37.87 

70.31 

38.17 

170.14 

38.48 

80 

81 

71.52 

38.03 

71.35 

33.34 

71.18 

38.65 

71.01 

33.96 

81 

82 

72.40 

38.50 

72.23 

38.81 

72.06 

39.13 

71.89 

39.44 

82 

83 

73.28 

38.97 

73.11 

39.29 

72.94 

39.60 

|72.77 

39.92 

83 

84 

74.17 

39.44 

73.99 

39.70 

73.82 

40.08 

73.64 

40.40 

84 

85 

75.05 

39.9 l 

74.88 

40.23 

74.70 

40.56 

74.52 

40.83 

85 

86 

75.93 

40.37 

75.76 

40.71 

75 58 

41.04 

75.40 

41.36 

86 

87 

76.82 

40.84 

70.64 

41.18 

76.46 

41.51 

76.28 

41.85 

87 

88 

77.70 

41.31 

7 7.52 

41 .65 

77.34 

41.99 

77.15 

42.33 

88 

89 

78.58 

41.78 

78.40 

42.13 

78.21 

42.47 

78.03 

42.81 

89 

90 

79.47 

42.25 

79.28 

42. GO 

79.09 

42.94 

78.91 

43.29 

90 

91 

80.35 

42.72 

SO. 10 

43.07 

79.97 

43.42 

79.78 

43.77 

91 

92 

81.23 

43.19 

81.04 

43.55 

80.85 

43.90 

80.66 

44.25 

92 

93 

82.11 

43.66 

81.92 

44.02 

81.73 

44.38 

8 1 .54 

44.73 

93 

94 

83.00 

44.13 

82.80 

44.49 

82.61 

44.85 

82.41 

45.21 

94 

95 

83.88 

44.60 

83.08 

44.97 

83.49 

45.33 

83.29 

!45.09 

95 

96 

84.70 

45.07 

84.57 

45.44 

84.37 

45.81 

84.17 

46.17 

90 

97 

85.65 

45.54 

85.45 

45.91 

85.25 

•46.28 

85.04 

|46.66 

97 

98 

86 .53 

40.01 

86 .33 

46.39 

86.12 

46.76 

85.92 

i 47.14 

98 

99 

87.41 

46.48 

87.21 

40.86 

87.00 

47.24 

80.80 

47.02 

99 

100 

88.29 

46.95 

88.09 

47.33 

87.88 

47.72 

87.67 

43.10 

100 

<*i 

o 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

c 

d 

w 

a? 

3 

4 

62 Deg. 

61f Deg. 

Cl£ Deg. 

6 U Deg. 

d 

ex. 

Q 






















































































































60 


TRAVERSE TABLE 


o 

5T 

tr+ 

p 

3 

o 

CD 

29 Deg. 

29} Deg. 

29^ Deg. 

29f 

Deg- 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.87 

0.48 

0.87 

0.49 

0.87 

0.49 

0.87 

0.50 

1 

2 

1.75 

0.97 

1.74 

0.98 

1.74 | 

0.98 

1.74 

0.99 

2 

3 

2.62 

1.45 

2.62 

1.47 

2.61 I 

1.48 

2.00 

1.49 

3 

4 

3.50 

1.94 

3.49 

1.95 

3.48 i 

1.97 

3.47 

1.98 j 

4 

5 

4.37 

2.42 

4.36 

2.44 

4.35 

2.46 

4.34 

2.48] 

5 

6 

5.25 

2.91 

5.23 

2.93 

5.22 

2.95 1 

5.21 

2.98 

6 

7 

6.12 

3.39 

6.11 

3.42 

6.09 

3.45 

0.03 

3.47 ] 

7 

8 

7.00 

3.88 

6.98 

3.91 

6.96 

3.94 

6.95 

3.97 

8 

9 

7.87 

4.36 

7.85 

4.40 

7.83 

4.43 

7.81 

4.47 

9 

10 

8.75 

4.85 

8.72 

4.89 

8.70 

4,92 

8.68 

4.90 

10 

11 

9.62 

5.33 

9.60 

5.37 

9.57 j 

5.42 

9.55 

5.46 

11 

12 

10.50 

5.82 

10.47 

5.86 

10.44 | 

5.91 

10.42 

5.95 

12 

13 

11.37 

6.30 

11.34 

6.35 

11.31 

6.40 

11.29 

6.45 

13 

14 

12.24 

6.79 

12.21 

6.84 

12.18 

6.89 

12.15 

6.95 

14 

15 

13.12 

7.27 

13.09 

7.33 

13.06 

7.39 

13.02 

7.44 

15 

16 

13.99 

7.76 

13.96 

7.82 

13.93 

7.88 

13.89 

7.94 

16 

17 

14.87 

8.24 

14.83 

8.31 

14.80 

8.37 

14.76 

8.44 

17 

18 

15.74 

8.73 

15.70 

8.80 

15.67 

8.86 

15.63 

8.93 

18 

19 

16.62 

9.21 

16.58 

9.28 

16.54 

9.36 

10.50 

9.43 

19 

20 

17.49 

9.70 

17.45 

9.77 

17.41 

9.85 

17.30 

9.92 

20 

21 

18.37 

10.18 | 

18.32 

10.20 

18.23 

10.34 

18.23 

10.42 

21 

22 

19.24 

10.67 | 

19.19 

10.75 

19.15 

10.83 

19.10 

10.92 

22 

23 

20.12 

11.15 

20.07 

11.24 

20.02 

11.33 

19.97 

11.41 

23 

24 

20.99 

11.64 

20.94 

11.73 

20.89 

11.82 

20.84 

11.91 

24 

25 

21.87 

12.12 

21.81 

12.22 

21.70 

12.31 

21.70 

12.41 

25 

26 

22.74 

12.60 

22.68 

12.70 

22.63 

12.80 

22.57 

12.90 

26 

27 

23.61 

13.09 

23.56 

13.19 

23.50 

13.30 

23.44 

13.40 

27 

28 

24.49 

13.57 

24.43 

13.68 

24.37 

13.79 

24.31 

13.89 

28 

29 

25.30 

14.06 

25.30 

14.17 

25.24 

14.28 

25.18 

14.39 

29 

30 

26. !?4 

14.54 

26.17 

14.06 

26.11 

14.77 

26.05 

14.89 

30 

31 

27.11 

15.03 

27.05 

15.15 

20.98 

15.27 

26.91 

15.38 

31 

32 

27.99 

15.51 

27.92 

15.64 

27.85 

15.76 

27.78 

15.88 

32 

33 

28.86 

16.00 

28.79 

16.12 

28.72 

16.25 

28.65 

16.38 

33 

34 

29.74 

16.48 

29.66 

16.61 

29.59 

16.74 

29.52 

16.87 

34 

35 

30.01 

16.97 

30.54 

17.10 

30.46 

17.23 

30.39 

17.37 

35 

36 

31.49 

17.45 

31.41 

17.59 

31.33 

17.73 

31.26 

17.86 

36 

37 

32.36 

17.94 

32.28 

18.08 

32.20 

18.22 

32.12 

18.36 

37 

38 

33.24 

18.42 

33.15 

18.57 

33.07 

18.71 

32.99 

18.86 

38 

39 

34.11 

18.91 

34.03 

19.06 

33.94 

19.20 

33.86 

19.35 

39 

40 

34.98 

19.39 

34.90 

19.54 

34.81 

19.70 

34.73 

19.85 

40 

41 

35.86 

19.88 

35.77 

20.03 

35.68 

20.19 

35.60 

20.34 

41 

42 

36.73 

20.30 

36.64 

20.52 

36.55 

20.68 

36.46 

20.84 

42 

43 

37.61 

20.85 

37.52 

21.01 

37.43 

21.17 

37.33 

21.34 

43 

44 

38.48 

21.33 

38.39 

21.50 

38.30 

21.07 

38.20 

21.83 

44 

45 

39.36 

21.82 

39.26 

21.99 

39.17 

22.10 

39.07 

22.33 

45 

46 

40.23 

22.30 

40.13 

22.48 

40.04 

22.05 

39.94 

22.83 

! 46 

47 

41.11 

22.79 

41.01 

22.97 

40.91 

23.14 

40.81 

23.32 

j 47 

48 

41.98 

23.27 

41.88 

23.45 

41.78 

23.08 

41.67 

23.82 

1 4S 

49 

42.86 

23.70 

42.75 

23.94 

42.65 

24.13 

42.54 

24.31 

I 49 

50 

43.73 

24.24 

43.62 

24.43 

43.52 

24.62 

43.41 

24.81 

| 50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

. Dep. 

Lat. 

Dep. 

[ Lat. 

i 6 

c_> 

! C 

1 61 

i 

Deg. 

60f Deg. 

60} Deg. 

1 

60} Deg. 

rt 

: '£ 

























































































































TRAVERSE TABLE 


01 


r 

a 

h— • 

w 

r-*- 

P - 

29 Deg. 

29} Deg. 

29|- Deg. 

29f Deg. 

O 

U) 

C"t* 

P 

S3 

O 

c 

Lat. | 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

CD 

51 

44.61 

24.73 

44.50 

24.92 

44.39 

25.11 

44.28 

25.31 

51 

52 

45.48 

25.21 

45.37 

25.41 

45.26 

25.61 

45.15 

25.80 

52 

53 

46.35 

25.69 

46.24 

25.90 

46.13 

26.10 

46.01 

26.30 

53 

54 

47.23 

26.18 

47.11 

26.39 

47.00 

26.59 

46.88 

26.80 

51! 

55 

48.10 

26.66 

47.99 

26.87 

47.87 

27.08 

47.75 

27.29 

55 j 

5C> 

48.98 

27.15 

48.80 

27.36 

48.74 

27.58 

48.62 

27.79 

56 

57 

49.85 

27.63 

49.73 

27.85 

49.61 

28.07 

49.49 

2S.28 

57 

5S 

50.73 

28.12 

50.60 

28.34 

50.48 

28.56 

50.36 

28.78 

58 

59 

51.60 

28.60 

51.48 

28.83 

51.35 

29.05 

51.22 

29.28 

59 

60 

52.48 

29.09 

52.35 

29.32 

52.22 

29.55 

52.09 

29.77 

60 

61 

53.35 

29.57 

53.22 

29.81 

53.09 

30.04 

52.96 

30.27 

61 

62 

54.23 

30.06 

54.09 

30.29 

63.96 

30.53 

53.83 

30.77 

62 

63 

55.10 

30.54 

54.97 

30.78 

54.83 

31.02 

54.70 

31.26 

63 

64 

55.98 

31.03 

55.84 

31.27 

55.70 

31.52 

55.56 

31.76 

64 

65 

56.85 

31.51 

56.71 

31.76 

56.57 

32.01 

56.43 

32.25 

65 | 

66 

57.72 

32.00 

57.58 

32.25 

57.44 

32.50 

57.30 

32.75 

66 1 

67 

58.60 

32.48 

58.46 

32.74 

58.31 

32.99 

58.17 

33.25 

67 

63 

59.47 

32.97 

59.33 

33.23 

59.18 

33.48 

59.04 

33.74 

68 

69 

60.35 

33.45 

60.20 

33.71 

60.05 

33.98 

59.91 

34.24 

69 

70 

61.22 

33.94 

61.07 

34.20 

60.92 

34.47 

60.77 

34.74 

70 

71 j 

-62.10 

34.42 

61.95 

34.69 

61.80 

34.96 

61.64 

35.23 

71 I 

72 

62.97 

34.91 

62.82 

35.18 

62.67 

35,45 

62.51 

35.73 

72 1 

73 

63.85 

35.39 

63.69 

35.67 

63.54 

35.95 

63.38 

36.22 

73 1 

74 

64.72 

35.88 

64.56 

36.16 

64.41 

36.44 

64.25 

36.72 

74 

75 

65.60 

36.38 

65.44 

36.65 

65.28 

36.93 

65.11 

37.22 

75 

76 

66.47 

36.85 

66.31 

37.14 

66.15 

37.42 

65.98 

37.71 

76 | 

77 

67.35 

37.33 

67.18 

37.62 

67.02 

37.92 

66.85 

38.21 

77 j 

78 

68.22 

37.82 

68.05 

38.11 

67.89 

38.41 

67.72 

38.70 

78| 

79 

69.09 

38.30 

68.93 

38.60 

68.76 

38.90 

68.59 

*89.20 

791 

80 

69.97 

38.78 

69.80 

39.09 

69.63 

39.39 

69 „46 

39.70 

80 

81 

70.84 

39.27 

70.67 

39.58 

70.50 

39.89 

70.32 

40.19 

81 

82 

71.72 

39.75 

71.54 

40.07 

71.37 

40.33 

71.19 

40.69 

82 

83 

72.59 

40.24 

72.42 

40.56 

72.24 

40.87 

72.06 

41.19 

83 

84 

73.47 

40.72 

73.29 

41.04 

73.11 

41.36 

72.93 

41.68 

84 

85 

74.34 

41.21 

74.16 

41.53 

73.98 

41.86 

73.80 

42.18 

85 

86 

75.22 

41.69 

75.03 

42.02 

74.85 

42.35 

74.67 

42.67 

86 

87 

76.09 

42.18 

75.91 

42.51 

75.72 

42.84 

75.53 

43.17 

87 

88 

76.97 

42.65 

76.78 

43.00 

76.59 

43.33 

76.40 

43.67 

88 

89 

77.84 

43.15 

77.65 

43.49 

77.46 

43.83 

77.27 

44.16 

89 

90 

78.72 

43.63 

78.52 

43.98 

78.33 

44.32 

78.14 

44.66 

90 

91 

79.59 

44.12 

79.40 

44.46 

79.20 

44.81 

79.01 

45.16 

91 

92 

80.46 

44.60 

80.27 

44.95 

80.07 

45.30 

79.87 

45.65 

> 92 

93 

81.34 

45.09 

81.14 

45.44 

80.94 

45.80 

80.74 

40.15 

; 93 

94 

82.21 

45.57 

82.01 

45.93 

81.81 

46.29 

81.61 

46.64 

! 94 

95 

83.09 

i 46.06 

82.89 

46.42 

82.68 

46.78 

I 82.48 

47.14 

95 I 

96 

83.96 

46.54 

83.76 

46.91 

83.55 

47.27 

183.35 

47.64 

! 96 1 

97 

84.84 

47.03 

84.63 

47.40 

84.42 

47.77 

l| 84.22 

!48.13 

97 

93 

85.71 

|47.51 

85.50 

47.88 

85.29 

48.20 

ji 85.08 

48.63 

98 

99 

86.59 

48.00 

86.38 

48.37 

86.17 

1 48 . 75 

lj 85.95 

49.13 

99 

100 

87.46 

148.48 

87.25 

48.86 

87.04 

49.24 

[86.82 

49 . 62 

100 

V 

e 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

0)’ 

a 

1 GO 

B a H 

| Q 

61 Deg. 

o 

i 

601 

Deg. 

| m 

1! 

Deg. 

j 00} Deg. 

l ! 

5 ! 


23 



































































































































TRAVERSE TABLE. 


G2 


O 
►— • 

If) 

30 Deg. 

301 Deg. 

304 

Deg. 

30| Deg. 

C 

5T 

c-*- 

p 

5 

O 

CD 

• 

L at. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

o 

1 

0.87 

0.50 

0 .S 6 

0.50 

0.86 

0.51 

0.86 

0.51 

1 

2 

1.73 

1.00 

1.73 

1.01 

1.72 

1.02 | 

1.72 

1.02 

2 

3 

2.00 

1.50 

2.59 

1.51 

2.53 

1.52, 

2.53 

1.53 

3 

4 

3.40 

2.00 

3.46 

2.02 

3.45 

2.03 ! 

3.44 

2.05 

4 

5 

4.33 

2.50 

4.32 

2.52 

4.31 

2.54 

4.30 

2.56 

5 

6 

5 .20 

3.00 

5.18 

3 .02 

5.17 

3.05 

5.16 

3.07 

6 

7 

0.00 

3.50 

6.05 

3.53 

6.03 

3.55 

6.02 

3.58 

7 

8 

G. 93 

4.00 

6.91 

4.03 

6.89 

4.06 

6.88 

4.09 

8 

9 

7.79 

4.50 

7.77 

4.53 

7.75 

4.57 

7.73 

4.60 

9 

10 

8.00 

5.00 

8.04 

5.04 

8.62 

5.08 

8 .59 

5.11 

10 

11 

9.53 

5.50 

9.50 

5.54 

9.48 

5.58 

9.45 

5.62 

11 

12 

10.39 

6.00 

10.37 

6.05 

10.34 

6.09 

10.31 

6.14 

12 

13 

11.26 

0.50 

11.23 

0.55 

11.20 

6.60 ! 

11.17 

6.65 

13 

14 

12.12 

7.00 

12.09 

7.05 

12.06 

7.11 

12.03 

7.16 

14 

15 

12.99 

7.50 

12.96 

7.56 

12.92 

7.61 

12.89 

7.67 

15 

16 

13.80 

8.00 

13.82 

8.06 

13.79 

8.12 

13.75 

8.18 

16 

17 

14.72 

8.50 

14.69 

8.56 

14.65 

8.63 

14.61. 

8.69 

17 

18 

15.59 

9.00 

15.55 

9.07 

15.51 

9.14 

15.47 

9 .20 

18 

19 

10.45 

9.50 

16.41 

9.57 

16.37 

9.64 

16.33 

9.71 

19 

20 

17.32 

10.00 ; 

17.23 

10.08 ! 

17.23 

10.15 

17.19 

10.23 

20 

21 

18.19 

10.50 

13.14 

10.58 

18.09 

10.66 

18.05 

10.74 

21 

22 

19.05 

11.00 

19.00 

11.03 i 

18.96 

11.17 

18.91 

11 .25 

22 

23 

19.9*2 

11.50 

19.87 

11.59 

19.82 

11.67 

19.77 

11.76 

23 

24 

20.78 

12.00 

20.73 

12.09 

20.68 

12.18 

20.63 

12.27 

24 

25 

21 .05 

12.50 

21.60 

12.59 i 

2 l. 54 

12.69 

21.49 

12.78 

25 

26 

r,o 

V • • > +* 

13.00 

22.46 

13.10 

22.40 

13.20 

22.34 

13.29 

26 

27 

23.38 

13.50 

23.32 

13.60 

23.26 

13.70 

23.20 

13.80 

27 

28 

24.25 

14.00 

24.19 

14.11 

24.13 

14.21 

24.06 

14.32 

28 

29 

25. 1 l 

14.50 

25.05 

14.61 

24.99 

14.72 

24.92 

14.83 

29 

30 

25.98 

15.00 

25.92 

15.11 

25.85 

15.23 

25.78 

15.34 

30 

31 

20.85 

13.50 

26.78 

15.62 

26.71 

15.73 

26.64 

15.85 

31 

32 

27.71 

16.00 

27.64 

16. 12 

27.57 

16.24 

127.50 

16.36 

32 

33 

28.58 

16.50 

28.51 

16.62 

28.43 

16.75 

28.36 

16.87 

33 

34 

29.44 

17.00 

29.37 

17.13 

29.30 

17.26 

29.22 

17.38 

34 

35 

30.31 

.17.50 

30.23 

17.63 

30.16 

17.76 

30.03 

17.90 

35 

30 

31.18 

18.00 

31.10 

18.14 

31.02 

18.27 

30.94 

13.41 

36 

37 

32.04 

18.50 

31.96 

18.64 

31.88 

18.78 

31.80 

18.92 

37 

38 

32.91 

19.00 

32.83 

19.14 

32.74 

19.29 

32.66 

19.43 

38 

39 

33.77 

19.50 

33.69 

19.65 

33.60 

19.79 

33.52 

19.94 

39 

40 

34.64 

20.00 

34.55 

20.15 

34.47 

20.30 

34.38 

20.45 

40 

41 

35.51 

20.50 

35.42 

20.65 

35.33 

20.81 

35.24 

20.98 

41 

42 

36.37 

21.00 

36.28 

21.16 

36. 19 

21.32 

36.10 

21.47 

42 

43 

37.24 

21.50 

37.14 

21.66 

37.05 

21.82 

36.95 

21.99 

43 

44 

38.11 

22.00 

38.01 

22.17 

37.91 

22.33 

37.81 

22.50 

44 

, 45 

38.97 

22.50 

33.87 

22.67 

38.77 

22.84 

3S. 67 

23.01 

45 

46 

39.34 

23.00 

139.74 

23.17 

39.63 

23.35 

39.53 

23.52 

46 

47 

40.70 

23.50 

40.60 

23.68 

40.50 

23.85 

40.39 

24.03 

47 

4S 

41.57 

24.00 

41.46 

24.18 

41.36 

24.36 

41 .25 

24.54 

48 

49 

42.44 

24.50 

42.33 

24.03 

42.22 

24.87 

42.11 

25.05 

49 

50 

43.30 

25.00 

43.19 

25. 19 

43.08 

25.38 

42.97 

25.50 

50 

<u 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

c 

rt 

—> 

w 

5 

CO Deg. 

59f Deg. 

50} 

Deg. 

59} 

Deo- 

7, 

! 



















































































































TRAVERSE TARLE 


S3 


D 

in 

p 

30 Deg. 

30£ Deg. 

30i Deg. 

o 

CO 

Deg. 

Distance. 

i 

o 

0 > 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

41.17 

25.50 

44.00 

25.69 

43.94 

25.88 

43.83 

2G.08 

51 

52 

45.03 

20.00 

44.92 

23.29 

i44.80 

26.39 

44.69 

26.59 

52 

• 53 

45.90 

20.50 

45.78 

23.70 

I 45.07 

26.90 

45.55 

27.10 

53 

54 

40.77 

27.00 

46.65 

27.29 

|40.53 

27.41 

40.41 

27.61 

54 

55 

47.03 

27.50 

47.51 

27.71 

|47.39 

27.91 

47.27 

28.12 

55 

56 

48.50 

28.00 

48.37 

23.21 

;48.25 

28.42 

48.13 

28.63 

50 

57 

49.30 

28.50 

49.24 

28.72 

! 49.1 I 

28.93 

48.99 

29.14 

57 

58 

50.23 

29.00 

50.10 

29.2 > 

49.97 

29.44 

49.85 

29.05 

58 

59 

51.10 

29.50 

50.97 

29.72 

:50.84 

29.94 

50.70 

30.17 

59 

00 

51.90 

3u. 00 

51.83 

30.23 

;51.70 

30.45 

51 . 56 

30.08 

60 

61 

52.83 

30.50 

52.69 

30.73 

!52 . 50 

30.96 

52.42 

31.19 

61 

62 

53.69 

31.00 

53.56 

31 .23 

!53.42 

31.47 

53.28 

31.70 

02 

03 

54.56 

31.50 

54.42 

3 t. 74 

i54.28 

31.97 

54.14 

32.21 

03 

04 

55.43 

32.00 

55.29 

32.24 

j55.14 

32.48 ! 

55.00 

32.72 

04 

65 

56.29 

32.50 

56.15 

32.75 

!50.01 

32.99 ! 

55.86 

33.23 

65 

00 

57.16 

33.00 

57.01 

33.25 

;50.87 

33.50 

50.72 

33.75 

06 

07 

58.02 

33.50 

57.88 

33.75 

: t>7.73 

34.01 

57.58 

34.26 

67 

03 

58.89 

34.00 

58.74 

34.26 

,58.59 

34.51 1 

58.44 

o4.77 

08 

09 

59.70 

34.50 

59.00 

34.76 

59.45 

35.02 1 

59.30 

35.28 

69 

'7U 

00.02 

35.001 

GO.47 

35.26 

60.31 

35.53 | 

00.16 

35.79 

70 

71 

01.49 

35.50 , 

61.33 

35.77 

01.18 

36.04 j 

61.02 

30.30 

71 

72 

02.35 

30.00 

62.20 

36.27 

62.04 

36.54 1 

61.88 

30.81 

72 

73 

03.22 

30.50 j 

63.06 

30.78 

1 62.90 

37.05 ; 

02.74 

27.32 

73 

74 

04.09 

37.00 

63.92 

37.28 

:63.76 

37.56 

03.00 

37.84 

74 

*- 

/;> 

04.95 

37.50 

; 64.79 

37.78 

i04.62 

38.07 

64.40 

38.35 

75 

70 

05.82 

38.00 

65.65 

38.29 

65.48 

38.57 

65.31 

38.80 

70 

77 

60.08 

38.50 

66.52 

38.79 

!66.35 
07.21 

39.08 

06.17 

39.37 

77 

78 

07.55 

39.00 

67.38 

39.29 

39.59 

07.03 

39.88 

78 

79 

68.42 

39.50 

08.24 

39.80 

68.07 

40.10 

67.89 

40.39 

79 

80 

69.28 

40.00 

69.11 

40.30 

08.93 

40.00 

63.75 

40.90 

80 

81 

70. 15 

40.50 

69.97 

10.81 

09.79 

41.11 

69 .Til 

41.41 

81 

82 

71.01 

41.00 

70.83 

41.31 

!70.05 

41.02 

70.47 

4 1 .93 

82 

83 

71.88 

41 .50 

71 ,70 

41.81 

! 71.52 

42.13 

71.33 

42.44 

S3 

84 

72.75 

42.00 

72.56 

42.32 

72.33 

42.03 

72.19 

42.95 

84 

85 

73.61 

42.50 

73.43 

42.82 

73.24 

4.3.14 

73.05 

43.46 

85 

SO 

74.48 

43.00 

74.29 

43.32 

174.10 

43.65 

73.91 

43.97 

80 

87 

75.34 

43.50 

75.15 

43.83 

174.96 

44.10 

74.77 

44.48 

87 

88 

76.21 

44.00 

76.02 

44.33 

175.82 

44.60 

75.63 

44.99 

88 

89 

77.08 

44.50 

70.88 

44.84 

76.08 

45. 17 

76.49 

45.51 

89 

90 

77.94 

45.00 

77.75 

45.34 

77.55 

45.08 

77.35 

46.02 

90 

91 

78.81 

45.50 

78.01 

45.84 

78.41 

40.19 

78.21 

40.53 

91 

92 

79.67 

4G.00 

79.47 

48.35 

79.27 

40.69 

79.07 

47.04 

92 

93 

80.54 

40.50 

80.34 

46.85 

80.13 

47.20 

79.92 

47.55 

93 

94 

81.41 

47.00 

81.20 

47.35 

80.99 

47.71 

80.78 

48.06 

94 

95 

82.27 

47.50 

82.06 

47.86 

81 .85 

48.22 

81.04 

48.57 

95 

96 

83*. 14 

48.00 

82.93 

48.36 

82.72 

48.72 < 

82.50 

49.08 

96 

97 

84.00 

48.50 

83.79 

48.87 

83.58 

49.23 

83.36 

49.00 

97 

98 

84.87 

49.00 

84.66 

49.37 

84.44 

49.74 

84.22 

50.11 

98 

99 

85.74 

49.50 

85.52 

49.87 

85.30 

50.25 

85.08 

50.02 

99 

100 

86.60 

50.00 

86.38 

50.38 

86.10 

50.75 

S5.94 

51.13 

100 

6 

CJ 

c 

Dep. 

Lat. 

Dep. 

Lat. 

1 i 

Dep. 

Lat. 

Dep, 

Lat. 

6 

o 

<~2 

rt 

Hi 

60 Deg. 

59] Deg. 

! 

59^ Deg. 

59-i Deg. 

i 










































































































TRAVERSE TABLE 


<)4 


Distance. 

'! 

31 Deg. 

3U Deg. 

31 ^ Deg. 

31f Deg. 

C 

05* 

r-*- 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat* 

Dep. 

Lat. 

Dep. 

3 

o 

? 

1 

0.86 

0.51 

0.85 

0.52 

0.85 

0.52 

0.85 

0.53 

1 

2 

1.71 

1.03 

1.71 

1.04 

1.71 

1.04 

1.70 

1.05 

2 

3 

2.57 

1.55 

2.56 

1.56 

2.56 

1.57 

2.55 

1.58 

3 

4 

3.43 

2.06 

3.42 

2.08 

3.41 

2.09 

3.40 

2.10 

4 

5 

4.2.9 

2.58 

4.27 

2.59 

4.26 

2.61 

4.25 

2.63 

5 

G 

5.14 

3.09 

5.13 

3.11 

5.12 

3.13 

5.10 

3.16 

6 

7 

6.00 

3.61 

5.98 

3.63 

5.97 

3.66 

5.95 

3.68 

7 

8 

6.86 

4.12 

6.84 

4.15 

6.82 

4.18 

6.80 

4.21 

8 

0 

7.71 

4.64 

7.G9 

4.67 

7.67 

4.70 

7.65 

4.74 

9 

10 

8.57 

5.15 

8.55 

5.19 

8.53 

5.22 

8.50 

5.26 

10 

11 

9.43 

5.67 

9.40 

5.71 

9.38 

5.75 

9.35 

5.79 

11 

12 

10.29 

6.18 

10.26 

6.23 

10.23 

6.27 

10.20 

6.31 

12 

13 

11.14 

6.70 

11.11 

6.74 

11.08 

6.79 

11.05 

6.84 

13 

14 

12.00 

7.21 

11.97 

7.26 

11.94 

7.31 

11.90 

7.37 

14 

15 

12.86 

7.73 

12.82 

7.78 

12.79 

7.84 

12.76 

7.99 

15 

16 

13.71 

8.24 

13.68 

8.30 

13.64 

8.36 

13.61 

8.42 

16 

17 

14.57 

8.76 

14.53 

8.82 

14.49 

8.88 

14.46 

8.95 

17 

18 

15.43 

9.27 

15.39 

9.34 

15.35 

9.40 

15.31 

9.47 

18 

19 

16.29 

9.79 

16.24 

9.86 

16.20 

9.93 

16.46 

10.00 

19 

20 

17.14 

10.30 

17.10 

10.38 

17.05 

10.45 

17.01 

10.52 

20 

21 

18.00 

10.82 

17.95 

10.89 

17.91 

10.97 

17.86 

11.05 

21 

22 

18.86 

11.33 

18.81 

11.41 

18.76 

11.49 

18.71 

11.58 

22 

23 

19.71 

11.85 

19.66 

11.93 ! 

19.61 

12.02 

19.56 

12.10 

23 

24 

20.57 

12.36 

20.52 

12.45 1 

20.46 

12.54 

20.41 

12.63 

24 

25 

21.43 

12.88 

21.37 

12.97 j 

21.32 

13.06 

' 21.26 

13.16 

25 

26 

22.29 

13.39 

22.23 

13.49 ! 

22.17 

13.58 

22.11 

13.68 

26 

27 

23.14 

13.91 

23.08 

14.01 

23.02 

14.11 

22.96 

14.21 

27 

28 

24.00 

14.42 

23.94 

14.53 

23.87 

14.63 

23.81 

14.73 

28 

29 

24.86 

14.94 

24.79 

15.04 

24.73 

15.15 

24.66 

15.26 

29 

30 

25.71 

15.45 

25.65 

15.56 j 

25.58 

15.67 

25.51 

15.79 

30 

31 

26.57 

15.97 

26.50 

16.08 

26.43 

16.20 

i26.36 

16.31 

31 

32 

27.43 

16.48 

27.36 

16.60 

27.28 

16.72 

27.21 

16.84 

32 

33 

28.29 

17.00 

28.21 

17.12 

28.14 

17.24 

i 28 . 06 

17.37 

33 

34 

29.14 

17.51 

29.07 

17.64 

23.99 

17.76 

128.91 

17.89 

34 

35 

30.00 

18.03 

29.92 

18.16 

29.84 

13.29 

129.76 

18.42 

35 

36 

30.86 

18.54 

30.78 

'18.68 

30.70 

18.81 

130.61 

18.94 

36 

37 

31.72 

19.06 

31.63 

19.19 

31.55 

19.33 

1 31.46 

19.47 

37 

38 

32.57 

19.57 

32.49 

19.71 

32.40 

19.85 

32.31 

20.00 

38 

39 

33.43 

20.09 

33.34 

20.23 

33.25 

20.38 

33.16 

20.52 

39 

40 

34.29 

20.60 

34.20 

20.75 

34.11 

20.90 

34.01 

21.05 

40 

41 

35.14 

21.12 

35.05 

21.27 

34.96 

21.42 

134.86 

21.57 

41 

42 

36.00 

21.63 

35.91 

21.79 1 

35.81 

21.94 

35.71 

22.10 

42 

43 

36.86 

22.15 

33.76 

22.31 

36.66 

22.47 

36.57 

22.63 

43 

44 

37.72 

22.66 

37.62 

22.831 

37.52 

22.99 

1 37.42 

23.15 

44 

45 

33.57 

23.18 

38.47 

23.341 

38.37 

23.51 

38.27 

23.68 

45 

46 

39.43 

23.69 

39.33 

23.86 

39.22 

24.03 

139.12 

24.21 

46 

47 

40.29 

24.21 

40.18 

24.38 

40.07 

24.56 

39.97 

24.73 

47 

48 

41.14 

24.72 

41.04 

24.90 

40.93 

25.08 

40.82 

25.26 

48 

49 

42.00 

25.24 

41.89 

25.42 

41.78 

25.60 

41.67 

25.78 

49 

50 

42.86 

25.75 

42.75 

25.94 

42.63 

26.12 

142.52 

26.31 

50 

6 

V 

a 

Dop. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

G 

cd 

00 

Q 

59 Deg. 

58f Deg. 

i 

58^ Deg. 

! 531 

1 

1 

Deg. 

cd 













































































































TRAVERSE TABLE 


65 


5 

CO 

6 

31 Deg. 

31* 

Deg. 

’ 314 

Deg. 

31| Deg. 

O 

5T 

p 

3 

O 

CD 

L 

at. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

D 

O 

CD 

51 

43 

.72 

26. 

27 

43.60 

26.46 

43.48 

26.65 

43. 

37 

26.84 

51 

52 

44 

.57 

26. 

78 

44.46 

26.98 

44.34 

27.17 

44. 

22 

27.36 

52 

53 

45 

.43 

27. 

30 

45.31 

27.49 

45.19 

27.69 

45. 

07 

27.89 

53 

54 

46 

.29 

27. 

81 

46.17 

28.01 

46.04 

28.21 

45. 

92 

28.42 

54 

55 

47 

.14 

28. 

33 

47.02 

28.53 

46.90 

28.74 

46. 

77 

28.94 

55 

56 

4S 

.00 

28. 

84 

47.88 

29.05 

47.75 

29.26 

47. 

62 

29.47 

56 

57 

48 

.86 

29. 

36 

48.73 

29.57 

48.60 

29.78 

48. 

47 

29.99 

57 

58 

49 

.72 

29. 

87 

49.58 

30.09 

49.45 

30.30 

49. 

32 

30.52 

58 

59 

50 

.57 

30. 

39 

50.44 

30.61 

50.31 

30.83 

50. 

17 

31.05 

59 

60 

51 

.43 

30. 

90 

51.29 

31.13 

51.16 

31 .35 

51. 

02 

31.57 

60 

61 

52 

.29 

31. 

42 

52.15 

31.65 

52.01 

31 .87 

51. 

87 

32.10 

61 

62 

53 

.14 

31. 

93 

53.00 

32.16 

52.86 

32.39 

52. 

72 

32.63 

62 

63 

54 

.00 

32. 

45 

53.86 

32.68 

53.72 

32.92 

53. 

57 

33. 15 

63 

64 

54 

.86 

32. 

96 

54.71 

33.20 

54.57 

33.44 

54. 

42 

33.68 

64 

65 

55 

.72 

33. 

48 

55.57 

33.72 

55.42 

33.96 

55. 

27 

34.20 

65 

66 

56 

.57 

33. 

99 

56.42 

34.24 

56.27 

34.48 

56. 

12 

34.73 

66 

67 

57 

.43 

34. 

51 

57.28 

34.76 

57.13 

35.01 

56. 

98 

35.26 

67 

68 

58 

.29 

35. 

02 

58.13 

35.28 

57.98 

35.53 

57. 

82 

35.78 

68 

69 

59 

14 

35. 

54 

58.99 

35.80 

58.83 

36.05 

58. 

67 

36.31 

69 

70 

60 

.00 

36. 

05 

59.84 

36.31 

59.68 

36.57 

59 

52 

36.83 

70 

71 

60 

.86 

36. 

57 

60.70 

36.83 

60.54 

37.10 

60. 

37 

37.36 

71 

72 

61 

.72 

37. 

08 

61.55 

37.35 

61.39 

37.62 

61 

23 

37.89 

72 

73 

62 

.57 

37. 

60 

62.41 

37.87 

62.24 

38.14 

62. 

08 

3S.41 

73 

74 

63 

.43 

38. 

11 

63.26 

38.39 

63.10 

38.66 

62 

93 

38.94 

74 

75 

64 

.29 

38. 

63 

64.12 

38.91 

63.95 

39.19 

63 

78 

39.47 

75 

76 

65 

.14 

39. 

14 

64.97 

39.43 

64.80 

39.71 

64 

63 

39.99 

76 

77 

66 

.00 

39. 

66 

65.83 

39.95 

65.65 

40.23 

65 

48 

40.52 

77 

78 

66 

.86 

40. 

17 

66.68 

40.46 

66.51 

40.75 

66 

33 

41.04 

78 

79 

67 

.72 

40. 

69 

67.54 

40.98 

67.36 

41.28 

67 

18 

41.57 

79 

80 

68 

.57 

41. 

20 

68.39 

41.50 

68.21 

41.80 

68 

03 

42. 10 

80 

81 

69 

.43 

41. 

72 

69.25 

42.02 

69.06 

42.32 

68 

88 

42.62 

81 

82 

70 

.29 

42. 

23 

70.10 

42.54 

69.92 

42.84 

69 

73 

43.15 

82 

83 

71 

.14 

42. 

75 

70.96 

43.06 

70.77 

43.37 

70 

58 

43.68 

83 

84 

72 

.00 

43. 

26 

71.81 

43.58 

71.62 

43.89 

71 

43 

44.20 

84 

85 

72 

.86 

43. 

78 

72.67 

44.10 

72.47 

44.41 

72 

.28 

44.73 

85 

86 

73 

.72 

44. 

29 

73.52 

44.61 

73.33 

44.93 

73 

.13 

45.25 

36 

87 

74 

.57 

44. 

81 

74.38 

45.13 

74.18 

45.46 

73 

.98 

45.78 

87 

88 

75 

.43 

45. 

32 

75.23 

45.65 

75.03 

45.98 

74 

.83 

46.31 

88 

89 

76 

.29 

45 

84 

76.09 

46.17 

75.88 

46.50 

75 

.68 

46.83 

89 

90 

77 

.15 

46 

35 

76.94 

46.69 

76.74 

47.02 

76 

.53 

47.36 

90 

91 

78 

.00 

46 

87 

77.80 

47.21 

77.59 

47.55 

1 77 

.38 

47.89 

91 

92 

78 

.86 

47. 

38 

78.65 

47.73 

78.44 

48.07 

78 

.23 

48.41 

92 

93 

79 

.72 

47 

90 

79.51 

48.25 

79.30 

48.59 

79 

.08 

48.94 

93 

94 

80 

.57 

48 

41 

80.36 

48.76 

80.15 

49.11 

1 79 

.93 

49.47 

94 

95 

81 

.43 

48 

93 

81.22 

49.28 

81.00 

49.64 

80 

.78 

49.99 

95 

96 

82 

.29 

49 

44 

82.07 

49.80 

81.85 

50.16 

1 81 

.63 

50.52 

96 

97 

83 

.15 

49 

96 

82.93 

50.32 

82.71 

50.68 

I 82 

.48 

51.04 

97 

98 

84 

.00 

50 

47 

83.78 

50.84 

83.56 

51.20 

83 

.33 

151.57 

| 98 

99 

84 

.86 

50 

.99 

84.64 

51.36 

84.41 

51.73 

84 

.18 

52.10 

99 

100 

85 

.72 

51 

.50 

85.49 

51.88 

85.26 

52.25 

85 

.04 

52.62 

100 

05 

O 

S3 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

4) 

O 

a 

d 

r/} 

• 

a 

f 


59 Deg 


58f 

Deg. 

584 

Deg. 

58* 

Deg. 

ce 

5 

























































































































CO 


TRAVERSE TABLE 


►— • 

; c/) 

r-+- 

32 Deg. 

32i Deg. • 

32 j 

Deg. 

32f Deg. 

Dista 

3 

o 

a 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

uat. 

Dep. 

D 

Q 

P 

r 

0.85 

0.53 

0.85 

0.53 

0.84 

0.54 

0.84 

0.54 

1 

9 

1.70 

1.06 

1.69 

1.07 

1.69 

1.07 

1.68 

1.08 

2 

3 

2.54 

1.59 

2.54 

1.60 

2.53 

1 .01 

2.52 

1.62 

3 

4 

3.39 

2.12 

3.38 

2.13 

3.37 

2.15 

3. 56 

2.16 

4 

5 

4.24 

2.65 

4 . 23 

2.67 

4.22 

2.69 

4.21 

2.70 

5 

0 

5.09 

3. 18 

5.07 

3 . 20 

5.06 

3 .22 

5.05 

3 . 25 

6 

7 

5.94 

3.71 

5.92 

3.74 

5.90 

3.76 

5.89 

3.79 

*7 

8 

C. 78 

4.24 

6 .77 

4.27 

6 .75 

4.30 

6 .73 

4.33 

8 

9 

7 . 63 

4.77 

7.61 

4.80 

7.59 

4.84 

7.57 

4.87 

9 

10 

8.48 

5.30 

8.46 

5.34 

8.43 

5.37 

8.41 

5.41 

10 

11 

9.33 

5.83 

9.30 

5.87 

9.28 

5.91 

9.25 

5.95 

11 

12 

10.13 

6.36 

10.15 

6.40 

10.12 

6.45 

10.09 

6.49 

12 

13 

11.02 

6.89 

10.99 

6.94 

10.96 

6.98 | 

10.93 

7.03 

13 

14 

11 .87 

7.42 

11.84 

7.47 

11.81 

7.52 ; 

11.77 

7.57 

14 

15 

12.72 

7.95 

12.69 

8.00 

12.65 

8.06 

12.62 

8.11 

15 

10 

13.57 

8.48 

13.53 

8 .54 

13.49 

8.601 

13.46 

8 .60 

16 

17 

14.42 

9.01 

14.38 

9.07 

14.34 

9.13 i 

14.39 

9 .20 

17 

18 

15.26 

9.54 

15.22 

9.61 

15. 18 

9.67! 

15.1*4 

9.74 

18 

19 

16. 11 

lo.or ; 

16.07 

10.14 j 

16.02 

10.21 i 

15.98 

10.28 

19 

20 

16.96 

10.60 j 

16.91 

10.67 1 

16.87 

10.75 ! 

16.82 

10.82 

20 

21 

17.81 

11.13; 

17.76 

l 1.21 j 

17.71 

11.28' 

17.66 

11.36 

21 

22 

18.66 

11.66 

18.61 

1 1.74 1 

18.55 

11.82 

13.50 

1 1.90 

22 

23 

19.51 

12.19 ! 

19.45 

12.27 

19.40 

12.36 

19.34 

12.44 

23 

24 

20.35 

12.72 

120.30 

12.81 

20.24 

12.30 

20.18 

12.93 

24 

25 

21.20 

13.25 

21.14 

13.34 

21 .03 

13.43 

21.03 

13.52 

25 

2 G 

22.05 

13.78 

21.99 

13.87 

21 . 93 

13.97 

21.87 

14.07 

26 

27 

22.90 

14.31 

22.83 

14.41 

22.77 

14.51 

22.71 

14.01 

27 

28 

23.75 

14.84 

23 . 68 

14.94 | 

23.61 

15.04 i 

23 . 55 

15.15 

28 

29 

24 . 59 

15.37 

24.53 

15.47i 

24.46 

15.58 i 

24.39 

15.69 

29 

30 

25.44 

15.90 

i25.37 

16.01 1 

25 .30 

16.12 

25.23 

16.23 

30 

31 

26.29 

16.43 

26.22 

16.54 

26. 15 

16.66 

26.07 

16.77 

31 

32 

27. 14 

16.96 

27.06 

17.03 

26.99 

17.19 

26.91 

17.31 

32 

33 

27.99 

17.49 

27.91 

17.61 

27.83 

17.73 

27.75 

17.85 

33 

34 

28.83 

18.02 

28.75 

18.14 

28.63 

18.27 j 

28.60 

18.39 

34 

35 

29.68 

18.55 

29.60 

18.68 

29.52 

18.81 i 

29.44 

18.93 

35 

36 

30.53 

19.08 

30.45 

19.21 

30.36 

19.34 : 

39.28 

19.48 

36 

37 

31 . 33 

19.61 

31.29 

19.74 

31.21 

19.88 

31.12 

20.02 

37 

38 

32.23 

20.14 

32.14 

20.23 

32.05 

20.42 

31.96 

20.56 

38 

39 

33.07 

20.67 

32.98 

20.81 

32.89 

20.95 

32.80 

21.10 

39 

40 

33.92 

21.20 

33.83 

21 .34 

33.74 

21.49 

33.64 

21.64 

40 

41 

34.77 

21.73 

34.67 

21.88 

34.58 

22.03 

34.43 

22.18 

41 

42 

35.62 

22.26 

35.52 

22.41 

35.42 

22.57 

35.32 

22.72 

42 

43 

36.47 

22 . 79 

36 . 37 

22.95 

36.27 

23.10 

36.16 

23 . 26 

43 

44 

37.31 

23.32 

37.21 

23.48 

37.11 

23.64 

37.01 

23.80 

44 

45 

33.16 

23.85 

38.06 

24.01 

37.95 

24. 18 

37.85 

24.34 

45 

46 

39.01 

24.3S 

33.90 

24 . 55 

38 . 80 

24.72 

33.09 

24.88 

46 

47 

39.86 

24.91 

39 . 75 

25. OS 

39 . 64 

25.25 

39.53 

25.43 

47 

48 

40.71 

25.44 

40.59 

25 . 61 

40.48 

25 . 79 

40 . 37 

25.97 

48 

49 

41.55 

25.97 

41.44 

26.15 

41.33 

26.33 

41.21 

26.51 

49 

50 

42.40 

26.50 

42.29 

26.68 

42.17 

26.86 

42.05 

27.05 

50 

6 

V 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dop. 

Lat. 

O 

c 

c 

ri 

*-» 

w 

Q 

58 Deg. 

571 Deg. 

f 

57 j Deg. 

1 

571 Deg. 

ri 

4-i 

T. 









































































































67 


TKAVEl’SE TABLE. 


Distance.| 

32 Deg. 

O 

Deg. 

32^ Deg 


321 Deg 


| Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. ! 

Lat. 

Dep. 

51 

43 

.25 

27. 

03 

43. 

13 

27.21 

43. 

01 

27. 

40 

42. 

89 

27. 

59 

51 

52 

44 

.10 

27. 

56 

43. 

98 

27.75 

43. 

86 

27. 

94 

43. 

73 

28. 

13 

52 

53 

44 

.95 

28. 

09 

44. 

82 

28.28 

44. 

70 

28. 

48 

44. 

58 

28. 

67 

53 

54 

45 

.79 

28. 

62 

45. 

67 

2S.82 

45. 

54 

29. 

01 

45. 

42 

29. 

21 

54 

55 

46 

64 

29. 

15 

46. 

51 

29.35 

46. 

39 

29. 

55 

46. 

26 

29. 

75 1 

55 

56 

47 

.49 

29. 

68 

47. 

36 

29.88 

47. 

23 

30. 

09 

47. 

10 

30. 

29 

56 

57 

48 

.34 1 

30. 

21 

48. 

21 

30.42 

48. 

07 

30. 

63 

47. 

94 

30. 

84 

57 

58 

49 

19 

30. 

74 

49. 

05 

30.95 

48. 

92 

31 . 

16 

48. 

78 

31. 

38 

58 

59 

50 

.03 

31 . 

27 

49. 

90 

31.48 

49. 

76 

31. 

70 

49. 

62 

31 . 

92 

69 

60 

50 

.88 

31. 

80 

50. 

74 

32.02 

50. 

60 

32. 

24 

50. 

46 

32. 

46 

60 

61 

51 

.73 

32. 

33 

51. 

59 

32.55 

51 

45 

32. 

78 

51. 

30 

33. 

00 

61 

62 

52 

.58 

32. 

85 

52. 

44 

33.08 

52. 

29 

33. 

31 

52. 

14 

33. 

54 

62 

63 

53 

.43 

33. 

38 

53. 

2 S 

33.62 

53. 

13 

33. 

85 

52. 

99 

34. 

08 

63 

64 

54 

.28 

33. 

91 

54. 

13 

34.15 

53. 

98 

34. 

39 

53. 

83 

34. 

62 

64 

65 

55 

12 

34. 

44 

54 

97 

34.68 

54. 

82 

34. 

92 

54. 

67 

35 

16 

65 

66 

55 

.97 

34. 

97 

55. 

82 

35.22 

55 

66 

35. 

46 

55. 

51 

35 

70 

66 

67 

56 

.82 

35. 

50 

56. 

66 

35.75 

56 

51 

36. 

00 

56 

35 

36. 

25 

67 

68 

57 

.67 

36. 

03 

57. 

51 

36.29 

57. 

35 

36. 

54 

57. 

19 

36. 

79 

68 

69 

58 

.52 

36. 

56 

58 

36 

36.82 

58. 

19 

37. 

07 

58. 

03 

37. 

33 

69 

70 

59 

.36 

37. 

09 

59. 

20 

37.35 

59 

04 

37. 

61 

58. 

87 

37. 

87 

70 

71 

60 

.21 

37. 

62 

60. 

05 

37.89 

59 

88 

39. 

15 

59 

71 

38. 

41 

71 

72 

61 

.06 

38. 

15 

60. 

89 

38.42 

60 

72 

38. 

69 

60 

55 

38. 

95 

70 

1 Ai 

73 

61 

.91 

38. 

68 

61 

74 

38.95 

61 

57 

39. 

22 

61 

40 

39 

49 

73 

74 

62 

.76 

39. 

21 

62 

58 

39.49 

62 

41 

39 

76 

62 

24 

40 

03 

74 

75 

63 

.60 

39. 

74 

63 

43 

40.02 

63 

25 

40 

30 

! 63 

OS 

40 

57 

75 

76 

64 

45 

40. 

27 

64 

28 

40.55 

64 

.10 

40 

83 

63 

.92 

41 

11 

76 

77 

65 

.30 

40. 

80 

65 

12 

4 1.09 

64 

.94 

41 

37 

64 

76 

41 

65 

77 

78 

66 

. 15 

41. 

33 

65 

.97 

41.62 

65 

.78 

41 

91 

65 

.60 

42 

20 

78 

79 

67 

.00 

41. 

86 

66 

.81 

42.16 

66 

.63 

42 

45 

| 66 

.44 

42 

.74 

79 

80 

67 

.84 

42. 

39 

67 

.66 

42.69 

67 

.47 

42 

98 

67 

.28 

43 

.28 

80 

81 

68 

.69 

42. 

92 

68 

.50 

43.22 

68 

.31 

43 

52 

i 68 

.12 

43 

.82 

SI 

82 

69 

. 54 

43. 

45 

69 

.35 

43.76 

69 

.16 

44 

.06 

! 68 

.97 

44 

.36 

82 

83 

70 

.39 

43. 

98 

70 

.20 

44.29 

70 

.00 

44 

.60 

! 69 

.81 

44 

.90 

83 

84 

71 

.24 

44 

51 

71 

.04 

44.82 

! 70 

.84 

45 

.13 

i 70 

.65 

45 

.44 

84 

85 

72 

.08 

45. 

04 

71 

.89 

45.36 

71 

.69 

45 

.67 

1 71 

.49 

45 

.98 

85 

86 

1 -V 

.93 

45. 

57 

72 

.73 

45.89 

72 

.53 

46 

.21 

| 72 

.33 

46 

.52 

86 

87 

73 

.78 

46. 

10 

73 

.58 

46.42 

73 

.38 

46 

.75 

! 73 

. 17 

47 

06 

87 

88 

74 

.63 

46. 

63 

74 

.42 

46.96 

74 

.22 

47 

.28 

74 

.01 

47 

.61 

88 

89 

75 

.48 

47 

16 

75 

.27 

47.49 

75 

.06 

47 

.82 

i 74 

.85 

4S 

. 15 

89 

90 

76 

.32 

47 

69 

76 

.12 

48.03 

75 

.91 

48 

.36 

75 

.09 

48 

.69 

90 

91 

77 

.17 

48 

22 

76 

.96 

48.56 

76 

. 75 

48 

.89 

i 76 

.53 

49 

.23 

91 

92 

78 

.02 

48 

75 

77 

.81 

49.09 

77 

.59 

49 

.43 

77 

.38 

49 

77 

92 

93 

78 

.87 

49 

28 

78 

. 65 

4&.03 

78 

.44 

49 

.97 

78 

.22 

50 

.31 

93 

94 

79 

.72 

49 

81 

79 

.50 

50.16 

79 

.28 

50 

.51 

i 79 

.06 

50 

.85 

94 

95 

80 

. 56 

50 

34 

80 

.34 

50.69 

80 

. 12 

51 

.04 

i 79 

.90 

51 

.39 

95 

96 

81 

.41 

50 

87 

81 

. 19 

51.23 

80 

.97. 

51 

.58 

j 80 

.74 

51 

.93 

96 

97 

82 

.26 

51 

40 

82 

.04 

51.76 

81 

.81 

52 

. 12 

81 

.58 

52 

.47 

97 

98 

83 

.11 

51 

93 

82 

.88 

52.29 

82 

.65 

52 

.66 

! 82 

.42 

53 

.02 

98 

99 

83 

.96 

52 

46 

83 

.73 

52.83 

83 

.50 

53 

.19 

! 83 

.26 

Do 

. 56 

99 

100 

84 

.80 

| 52 

99 

84 

.57 

53.36 

84 

.34 

53 

.73 

j 84 

. 10 


. 10 

100 

e 

C 

rt 

72 

Q 

Dep. 

Lat. 

Dep. 

| Lat. 

Dep. 

Lat. 

Dep. 

T 

! 

at. 

1. 

Distance. 

( 

58 Deg. 

57| Deg. 

57i Deg. 

571 Deg. 







































































































G8 


TRAVERSE TABLE 


o 

in' 
<-► 

33 Deg. 

33£ Deg. 

33i Deg. 

33f Deg. 

o 

in 

c+ 

p 

P 

O 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

a 

1 

0.84 

0.54 

0.84 

0.55 

0.83 

0.55 

0.83 

0.56 

1 

2 

1.68 

1.09 

1.67 

1.10 

1.67 

1.10 

1.66 

1.11 

2 

3 

2.52 

1.63 

2.51 

1.64 

2.50 

1.66 

2.49 

1.67 

3 

4 

3.35 

2.18 

3.35 

2.19 

3.34 

2.21 

3.33 

2.22 

4 

5 

4.19 

2.72 

4.18 

2.74 

4.17 

2.76 

4.16 

2.78 

5 

G 

5.03 

3.27 

5.02 

3.29 

5.00 

3.31 

4.99 

3.33 

6 

7 

5.87 

3.81 

5.85 

3.84 

5.84 

3.86 

5.82 

3.89 

7 

8 

6.71 

4.36 

6.69 

4.39 

6.67 

4.42 

6.65 

4.44 

8 

9 

7.55 

4.90 

7.53 

4.93 

7.50 

4.97 

7.48 

5.00 

9 

10 

8.39 

5.45 

8,36 

5.48 

8.34 

5.52 

8.31 

5.56 

10 

11 

9.23 

5.99 

9.20 

6.03 

9.17 

6.07 

9.15 

6.11 

11 

12 

10.06 

6.54 

10.04 

6.58 

10.01 

6.62 

9.98 

S. 67 

12 

13 

10.90 

7.08 

10.87 

7.13 

10.84 

7.18 

10.81 

7.22 

13 

14 

11.74 

7.62 

11.71 

7.68 

11.67 

7.73 

11.64 

7.78 

14 

15 

12.58 

8.17 

12.54 

8.22 

12.51 

8.28 

12.47 

8.33 

15 

16 

13.42 

8.71 

13.38 

8.77 

13.34 

8.83 

13.30 

8.89 

16 

17 

14.26 

9.26 

14.22 

9.32 

14.18 

9.38 

14.13 

9.44 

17 

18 

15.10 

9.80 

15.05 

9.87 

15.01 

9.93 

14.97 

10.00 

18 

19 

15.93 

10.35 

15.89 

10.42 

15.84 

10.49 

15.80 

10.56 

19 

20 

16.77 

10.89 

16.73 

10.97 

16.68 

11.04 

16.63 

11.11 

20 

21 

17.61 

11.44 

17.56 

11.51 

17.51 

11.59 

17.46 

11.67 

21 

22 

18.45 

11.98 

18.40 

12.06 

IS. 35 

12.14 

18.29 

12.22 

22 

23 

19.29 

12.53 

19.23 

12.61 

19.18 

12.69 

19.12 

12.78 

23 

24 

20.13 

13.07 

20.07 

13.16 

20.01 

13.25 

19.96 

13.33 

24 

25 

20.97 

13.62 

20.91 

13.71 

20.85 

13.80 

20.79 

13.89 

25 

26 

21.81 

14.16 

21.74 

14.26 

21.68 

14.35 

21.62 

14.44 

26 

27 

22.64 

14.71 

22.58 

14.80 

22.51- 

14.90 

22.45 

15.00 

27 

28 

23.48 

15.25 

23.42 

15.35 

23.35 

15.45 

23.23 

15.56 

28 

29 

24.32 

15.79 

24.25 

15.90 

24.18 

16.01 

24.11 

16.11 

29 

30 

25.16 

16.34 

25.09 

16.45 

25.02 

16.58 

24.94 

16.67 

30 

31 

26.00 

16.88 

25.92 

17.00 

25.85 

17.11 

25.78 

17.22 

31 

32 

26.84 

17.43 

26.76 

17.55 

26.68 

17.66 

26.61 

17.78 

32 

33 

27.68 

17.97 

27.60 

18.09 

27.52 

18.21 

27.44 

IS. 33 

33 

34 

28.51 

18.52 

28.43 

18.64 

28.35 

18.77 

28.27 

13.89 

34 

35 

29.35 

19.06 

29.27 

19.19 

29.19 

19.32 

29.10 

19.44 

35 

36 

30.19 

19.61 

30.11 

19.74 

30.02 

19.87 

29.93 

20.00 

36 

37 

31.03 

20.15 

30.94 

20.29 

30.85 

20.42 

30.76 

20.56 

37 

38 

31.87 

20.70 

31.78 

20.84 

31.69 

20.97 

31.60 

21.11 

38 

39 

32 .71 

21.24 

32.62 

21.38 

32.52 

21.53 

32.43 

21.67 

39 

40 

33.55 

21.79 

33.45 

21.93 

33.36 

22.08 

33.26 

90 90 

A* +4 • av 

40 

41 

34.39 

22.33 

34.29 

22.48 

34.19 

22.63 

34.09 

22.78 

41 

42 

35.22 

22.87 

35.12 

23.03 

35.02 

23.18 

34.92 

23.33 

42 

43 

36.06 

23.42 

35.96 

23.58 

35.86 

23.73 

35.75 

23.89 

43 

44 

36.90 

23.96 

36.80 

24.12 

36.69 

24.29 

36.58 

24.45 

44 

45 

37.74 

24.51 

37.63 

24.67 

37.52 

24.84 

37.42 

25 00 

45 

46 

38.58 

25.05 

38.47 

25.22 

38.36 

25.39 

38.25 

25.56 

46 

47 

39.42 

25.60 

39.31 

25.77 

39.19 

25.94 

39.08 

26.11 

47 

48 

40.26 

26.14 

40.14 

26.32 

40.03 

26.49 

39.91 

26.67 

48 

49 

41.09 

26.69 

40.98 

26.87 

40.86 

27.04 

40.74 

27.22 

49 

50 

41.93 

27.23 

41.81 

27.41 

41.69 

27 . 60 

41.57 

27.78 

50 

d 

o 

£5 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

O 

c 

rf 

in 

Q 

57 Deg. 

56| Deg. 

56£ Deg. 

56J Dog. 

i£J 



































































































TRAVERSE TABLE 


69 


n 

w 

C0 

*H 

33 Deg. 

33} Deg. 

33-l 

Deg. 

33} Deg. 

Distance. 

2 

n 

a 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

42.77 

27.78 

42.65 

27.96 

42.53 

23.15 

42.40 

28.33 

51 

52 

43.61 

28.32 

43.49 

28.51 

43.36 

28.70 

43.24 

28.89 

52 

53 

44.45 

28.87 

44.32 

29.08 

44.20 

29.25 

44.07 

29.45 

53 

54 

45.29 

29.41 

45.16 

29.61 

45.03 

29.80 

44.90 

30.00 

54 

55 

46.13 

29.96 

46.00 

30.16 

45.86 

30.36 

45.73 

30.56 

55 

56 

46.97 

30.50 

46.83 

30.70 

46.70 

30.91 

46.56 

31.11 

56 

57 

47.80 

31.04 

47.67 

31.25 

47.53 

31.46 ; 

47.39 

31.67 

57 

58 

48.64 

31.59 

48.50 

31.80 

48.37 

32.01 

48.23 

32.22 

58 

59 

49.48 

32.13 

49.34 

32.35 

49.20 

32.56 

49.06 

32.78 

59 

60 

50.32 

32.68 

50.18 

32.90 

50.03 

33.12 

49.89 

33.33 

60 

61 

51.16 

33.22 

51.01 

33.45 

50.87 

33 . 67 

50.72 

33.89 

61 

62 

52.00 

33.77 

51.85 

33.99 

51.70 

34.22 

51.55 

34.45 

62 

63 

52.84 

34.31 

52.69 

34.54 

52.53 

34.77 

52.38 

35.00 

63 

64 

53.67 

34.86 

53.52 

35.09 

53.37 

35.32 

53.21 

35.56 

64 

65 

54.51 

35.40 

54.36 

35.64 

54.20 

35.88 

54.05 

36.11 

65 

66 

55.35 

35.95 

55.19 

36.19 

55.04 

36.43 

54.88 

36.67 

66 

67 

56.19 

36.49 

56.03 

36.74 

55.87 

36.98 

55.71 

37.22 

67 

68 

57.03 

37.04 

56.87 

37.28 

56.70 

37.53 

56.54 

37.78 

68 

69 

57.87 

37.58 i 

57.70 

37.83 

57.54 

38.08 

57.37 

33.33 

69 

70 

58.71 

38.12 

58.54 

38.38 

58.37 

3S. 64 

58.20 

38.89 

70 

71 

59.55 

38.67 

59.38 

38.93 j 

59.21 

39.19 

59.03 

39.45 

71 

72 

60.38 

39.21 

60.21 

39.48 ! 

60.04 

39.74 

59.87 

40.00 

72 

73 

61.22 

39.76 

61.05 

40.03 I 

60.87 

40.29 I 

60.70 

40.56 

73 

74 

62.06 

40.30 

61.89 

40.57 

61.71 

40.84 

61.53 

41.11 

74 

75 

62.90 

40.85 

62.72 

41.12 

62.54 

41.40 

62.36 

41.67 

75 

76 

63.74 

41.39 

63.56 

41.67 

63.38 

41.95 

63.19 

42.22 

76 

77 

64.58 

41.94 

64.39 

42.22 

64.21 

42.50 

64.02 

42.78 

77 

78 

65.42 

42.48 

65.23 

42.77 

65.04 

43.05 

64.85 

43.33 

73 

79 

66.25 

43.03 

66.07 

43.32 

65.88 

43.60 

65.69 

43.89 

79 

80 

67.09 

43.57 

66.90 

43.86 

66.71 

44.15 

66.52 

44.45 

80 

81 

67.93 

44. 12 

67.74 

44.41 

67.54 

44.71 

67.35 

45.00 

81 

82 

68.77 

44.66 

68.58 

44.96 

63.38 

45.26 

68.18 

45.56 

82 

83 

69.61 

45.20 

69.41 

45.51 

69.21 

45.81 

69.01 

46. 11 

83 

84 

70.45 

45.75 

70.25 

46.06 

70.05 

46.36 

69.84 

46.67 

84 

85 

71.29 

46.29 

71.08 

46.60 

70.88 

46.91 

70.67 

47.22 

85 

86 

72.13 

46.84 

71.92 

47.15 

71.71 

47.47 

71.51 

47.78 

86 

87 

72.96 

47.38 

72.76 

47.70 

72.55 

48.02 

72.34 

48.33 

87 

88 

73.80 

47.93 

73.59 

48.25 

73.38 

48.57 

73.17 

48.89 

88 

89 

74.64 

48.47 

74.43 

48.80 

74.22 

49.12 

74.00 

49.45 

89 

90 

75.48 

49.02 

75.27 

49.35 

75.05 

49.67 

74.83 

50.00 

• 90 

91 

76.32 

49.56 

76.10 

49.89 

75.88 

50.23 

75.66 

50.56 

91 

92 

77.16 

50.11 

76.94 

50.44 

76.72 

50.78 

176.50 

51.11 

92 

93 

78.00 

50.65 

77.77 

50.99 

77.55 

51.33 

i 77.33 

51.67 

93 

94 

78.83 

51.20 

78.61 

51.54 

78.39 

51.88 

!78.16 

52.22 

94 

95 

79.67 

51.74 

79.45 

52.09 

79.22 

52.43 

I 78.99 

52.78 

95 

96 

80.51 

52.29 

80.28 

52.64 

80.05 

52.99 

79.82 

53.33 

96 

97 

81.35 

52.83 

81.12 

53.18 

80.89 

53.54 

! 80.65 

53.89 

i 97 

98 

82.19 

53.37 

81.96 

53.73 

81.72 

54.09 

81.48 

54.45 

98 

99 

83.03 

53.92 

82.79 

54.28 

82.55 

54.64 

82 . 32 

55.00 

99 

100 

83.87 

54.46 

83.63 

54.83 

83.39 

55.19 

83.15 

55.56 

100 

6 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

‘ 

Dep. 

Lat. 

<x>‘ 

o 

c 

S/3 

»H 

3 

57 Deg. 

5 61 Deg. 

561 

- 

Deg. 

56} Deg. 

cc 

X 




















































































































70 


TRAVERSE TABLE. 


o 

ST 

r- 

P 

34 Deg. 

34i Deg. 

34^ Deg. 

34f Deg. 

C 

GC* 

P 

b 

o 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lut» 

Dep. 

Lat. 

Dep. 

3 

cd 

CD 

1 

0.83 

0.56 

0.83 

0.56 

0.82 

0.57 

0. 82 

0.57 

i 

2 

1.66 

1.12 

1.65 

1.13 

1.65 

1. 13 

1.64 

1.14 

2 

3 

2.49 

1.68 

2.48 

1.69 

2.47 

1.70 

2.46 

1.71 

3 

4 

3.32 

2.24 

3.31 

2.25 

3.30 

2.27 

3.29 

2.28 

4 

5 

4.15 

2.80 

4.13 

2.81 

4.12 

2.83 

4.11 

2.85 

5 

G 

4.97 

3.36 

4.96 

3.38 

4.94 

3.4-6 

4.93 

3.42 

<i 

7 

5.80 

3.91 

5.79 

3.94 

5.77 

3.96 

5.75 

3.99 

7 

8 

6.63 

4.47 

6.61 

4.50 

6 .59 

4.53 

6 .57 

4.56 

8 

9 

7.46 

5.03 

7.44 

5.07 

7.42 

5.10 

7.39 

5. 13 

9 

10 

8.29 

5.59 

8.27 

5.63 

8.24 

5.66 

8.22 

5.70 

10 

11 

9.12 

6 . 15 

9.09 

6.19 

9.07 

6.23 

9.04 

G.27 

11 

12 

9.95 

6.71 

9.92 

6.75 

9.89 

6.80 

9.86 

6.84 

12 

13 

10.78 

7.27 

1 0.75 

7.32 

10.71 

7.36 

10.68 

7.41 

13 

14 

11.61 

7.83 

11.57 

7.88 

1 1.54 

7.93 

11.50 

7.93 

14 

15 

12.44 

8.39 

12.40 

8.44 

12.36 

8.50 

12.32 

8 .55 

15 

16 

13.26 

8 .95 

13.23 

9.00 

13.19 

9.08 

13.15 

9.12 

16 

17 

11.09 

9.51 

14.05 

9.57 

14.01 

9.63 

13.97 

9.69 

17 

IS 

14.92 

10.07 

14.88 

10.13 

14.83 

10.20 

14.79 

10.26 

18 

19 

15.75 

10.62 

15.71 

10.69 

15.66 

10.76 

15.61 

10.83 

19 

20 

16.58 

11.18 

16.53 

11.26 

16.48 

11.33 

16.43 

11.40 

20 

21 

17.41 

11.74 

17.36 

11.82 

17.31 

11.89 1 

17.25 

11.97 

21 

22 

18.24 

12.30 

18.18 

12.38 

18.13 

12.46 

18.08 

12.54 

22 

23 

19.07 

12.86 

19.01 

12.94 

18.95 

13.03 | 

18.90 

13.11 

23 

24 

19.90 

13.42 

19.84 

13.51 

19.78 

13.59 

19.72 

13.68 

24 

25 

20.73 

13.98 

20.66 

14.07 

20.60 

14.16, 

20.54 

14.25 

25 

26 

21 .55 

14.54 

21.49 

14.63 

21.43 

14.73 

21.36 

14.82 

26 

27 

22.38 

15.10 

22.32 

15.20 i 

22.25 

15.29 

22 . 18 

15.39 

27 

28 

23.21 

15 66 

!23.14 

15.76 | 

23.08 

15.86 

23.01 

15.96 

28 

29 

24.04 

16.22 

23.97 

16.32 

23.90 

16.43 i 

23.83 

16.53 

29 

30 

24.87 

16.78 

24.80 

16.83 

24.72 

16.99 | 

24.65 

17.10 

30 

31 

25.70 

17.33 

25.02 

17.45 

25.55 

17.56 

25.47 

17.67 

31 

32 

26.53 

17.89 

26.45 

18.01 

26.37 

18.12 

26.29 

18.24 

32 

33 

27.36 

18.45 

27.23 

18.57 

27.20 

18.69 

27.11 

18.81 

33 

34 

28.19 

19.01 

28.10 

19.14 

28.02 

19.26 

27.94 

19.38 

34 

35 

29.02 

19.57 

i28.93 

19.70 

23.84 

19.82 

28.76 

19.95 

35 

36 

29.85 

2 ^. 13 

S 29.76 

20.26 

29.67 

20.39 

29.58 

20.52 

36 

37 

30.67 

20.69 

30.58 

20.82 

30.49 

20.96 

30.40 

21.09 

37 

38 

31.50 

21.25 

31.41 

21.39 

31.32 

21.52 

31.22 

21.66 

38 

39 

32.33 

21.81 

32.24 

21.95 

32. 14 

22.09 

32.04 

22.23 

39 

40 

33.16 

22.37 

33.06 

22.51 

32.97 

22.66 

32.87 

22.80 

40 

41 

33.99 

22.93 

33.89 

23.07 

33.79 

23.22 

33.69 

23.37 

41 

42 

34.82 

23.49 

34.72 

23.64 

34.61 

23.79 

34.51 

23.94 

42 

43 

35.65 

24.05 

35.54 

24.20 

35.44 

24.36 

35.33 

24.51 

43 

44 

36.48 

24.60 

36.37 

24.76 

36.26 

24.92 

36.15 

25.08 

44 

45 

37.31 

25.16 

37.20 

25.33 

37.09 

25.49 

36.97 

25.65 

45 

46 

38.14 

25.72 

38.02 

25.89 

37.91 

26.05 

37.80 

26.22 

46 

47 

i38.96 

26.28 

38.85 

26.45 

38.73 

26.62 

38.62 I 26.79 

47 

48 

39.79 

26.84 

39.68 

27.01 

39.56 

27.19 

39.44 

27.36 

48 

49 

40.62 

127.40 

40.50 

27.58 

40.38 

27.75 

40.26 

27.93 

49 

50 

41.45 

1 27.96 

41 .33 

2S. 14 

41.21 

28.32 

41.08 

28.50 

50 

o' 

o 

c 

Dep. 

Lat. 

Dep. 

| Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

rt 

Vi 

Q 

56 Deg. 

55$ Deg. 

55^ 

Deg. 

5 ^ 

Deg. 

ci 

V. 













































































































TRAVERSE TABLE. 


71 


o 

<y* 

r-*~ 

P 

1 

34 Deg. 

34| Deg. 

i 

341 

Deg. 

34| Deg. 

Distance. 

3 

O 

CD 

I,at. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

i42.23 

28.52 

42.16 

28.70 

42.03 

28.89 

41.90 

29.07 

51 

52 

i43.11 

29.08 

42.98 

29.27 

42.85 

29.45 

42.73 

29.64 

52 

53 

43.94 

29.64 

43.81 

29.83 

43.68 

30.02 

43.55 

30.21 

53 

54 

44.77 

30.20 

44.64 

30.39 

44.50 

30.59 

44.37 

30.78 

54 

55 

45.60 

30.76 

45.46 

30.95 

45.33 

31.15 

45.19 

31.35 

55 

56 

46.43 

31.31 

46.29 

31.52 

146.15 

3! . 72 

46.01 

31.92 

56 

57 

47.26 

31.87 

47.12 

32. OS 

46.98 

32.29 

46.83 

32.49 

57 

58 

43.08 

32.43 

47.94 

32.64 

147.80 

32.85 

47.66 

33.06 

58 

59 

48.91 

32.99 

48.77 

33.21 

48.62 

33.42 

48.48 

33.63 

59 

60 

49.74 

33.55 

49.60 

33.77 

49.45 

33.98 

49.30 

34.20 

60 

61 

50.57 

34.11 

50.42 

34.33 

50.27 

34.55 

50.12 

34.77 

61 

62 

51.40 

34.67 

51.25 

34.89 

51.10 

35.12 

50.94 

35.34 

62 

63 

52.23 

35.23 

52.08 

35.46* 

51.92 

35.68 

51.76 

35.91 

63 

64 

53.06 

35.79 

52.90 

36.02 

52.74 

36.25 

52.59 

36.48 

64 

65 

53.89 

36.35 

53.73 

36.58 

53.57 

36.82 

53.41 

37.05 

65 

66 

54.72 

36.91 

54.55 

37.15 

54.39 

37.38 

54.23 

37.62 

66 

67 

55.55 

37.46 

55.38 

37.71 

55.22 

37.95 

55.05 

38.19 

67 

68 

56.37 

38.03 

56.21 

38.27 

56.04 

33.52 

55.87 

38.76 

68 

69 

57.20 

38.58 

57.03 

38.83 

56.86 

39.08 

56.69 

39.33 

69 

70 

58.03 

39.14 

57.86 

39.40 

57.69 

39.65 

57.52 

39.90 

70 

71 

58.86 

39.70 

58.69 

39.96 

58.51 

40.21 

58.34 

40.47 

71 

72 

59.69 

40.26 

59.51 

40.52 

59.34 

40.78 

59. 16 

41.04 

72 

73 

60.52 

40.82 

60.34 

41 .08 

60.16 

41 .35 

59.98 

41.61 

73 

74 

61.35 

41.38 

61.17 

41.65 

60.99 

41.91 

60.80 

42.18 

74 

75 

62. 18 

41.94 

61.99 

42.21 

61 .81 

42.48 

61.62 

42.75 

75 

76 

63.01 

42.50 

62.82 

42.77 

62.63 

43.05 

62.45 

43.32 

76 

77 

63.84 

43.06 

63.65 

43.34 

63.46 

43.61 

63.27 

43.89 

77 

78 

64.66 

43.62 

64.47 

43.90 

64.28 

44.18 

64.09 

44.46 

78 

79 

65.49 

44. 18 

65.30 

44.46 

65.11 

44.75 

64.91 

45.03 

79 

80 

66.32 

44.74 

66.13 

45.02 

65.93 

45.31 

65.73 

45.60 

80 

81 

67.15 

45.29 

66.95 

45.59 

66.75 

45.88 

66.55 

46.17 

81 

82 

67.98 

45.85 

67.78 

46.15 

67.58 

46.45 

67.37 

46.74 

82 

83 

68.81 

46.41 

68.61 

46.71 

68.40 

47.01 

68.20 

47.31 

83 

84 

69.64 

46.97 

69.43 

47.28 

69.23 

47.58 

69.02 

47.88 

84 

85 

70.47 

47.53 

70.26 

47.84 

70.05 

48.14 

69.84 

48.45 

85 

86 

71.30 

48.09 

71.09 

48.40 

70.87 

48.71 

70.66 

40.02 

86 

87 

72.13 

48.65 

71.91 

48.96 

71.70 

49.28 

71.48 

49.59 

87 

88 

72.96 

49.21 

72.74 

49.53 

72.52 

49.84 

72.30 

50.16 

88 

89 

73.78 

49.77 

73.57 

50.09 

73.35 

50.41 

73.13 

50.73 

89 

90 

74.61 

50.33 

74.39 

50.65 

74.17 

50.98 

73.95 

51.30 

90 

91 

75.44 

50.89 

75.22 

51.22 

75.00 

51.54 

74.77 

51.87 

91 

92 

76.27 

51.45 

76.05 

51.78 

75.82 

52.11 

75.59 

52.44 

92 

93 

77.10 

52.00 

76.87 

52.34 

76.64 

52.68 

76.41 

53.01 

93 

94 

77.93 

52.56 

77.70 

52.90 

77.47 

53.24 

77.23 

53.58 

94 

95 

78.76 

53.12 

78.53 

53.47 

78.29 

53.81 

7S.06 

54. 15 

95 

96 

79.59 

53.68 

79.35 

54.03 

79.12 

54.37 

78.88 

54.72 | 

96 

97 

80.42 

54.24 

SO. 18 

54.59 

79.94 

54.94 

79.70 

55.29 

97 

98 

81.25 

54.80 

81.01 

55.15 

80.76 

55.51 

80.52 

55.86 

98 

99 

82.07 

55.36 

81.83 

55.72 

81.59 

56.07 

81.34 

56.43 

99 

too 

82.90 

55.92 

82.66 

56.28 

82.41 

56.64 

82.16 

57.00 

100 

d 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

d 

o 

G 

Distc 

56 Deg. 

55f Deg. 

55^ Deg. 

55\ Deg. 

c3 

72 

5 










































































































72 


TRAVERSE TABLE 


o 

m' 

<-► 

35 Deg. 

35i Deg. 

35i Deg. 

35J Deg. 

2 

55* 

r*> 

P3 

s 

o 

<D 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

ra 

1 

0.82 

0.57 

0.82 

0.58 

0.81 

0.58 

0.81 

0.58 

1 

o 

1.64 

1.15 

1.63 

1.15 

l. 63 

1.16 

1.62 

] .17 

2 

3 

2.46 

1.72 

2.45 

1.73 

2.44 

1.74 

2.43 

1.75 

3 

4 

3.28 

2.29 

3.27 

2.31 

3.28 

2.32 

3.25 

2.34 

4 

5 

4.10 

2.87 

4.08 

2.89 

4.07 

2.90 

4.06 

2.92 

5 

6 

4.91 

3.44 

4.90 

3.46 

4.88 

3.48 

4.87 

3.51 

G 

7 

5.73 

4.01 

5.72 

4.04 

5.70 

4.08 

5.68 

4.09 

7 

8 

6.55 

4.59 

6.53 

4.62 

6.51 

4.65 

6.49 

4.07 

8 

9 

7.37 

5.16 

7.35 

5.19 

7.33 

5.23 

7.30 

5.26 

9 

10 

8.19 

5.74 

8.17 

5.77 

8.14 

5.81 

8.12 

5.84 

10 

11 

9.01 

6.31 

8.98 

6.35 

8.96 

6.39 

8.93 

6.43 

11 

12 

9.83 

6.88 

9.80 

6.93 

9.77 

6.97 

9.74 

7.01 

12 

13 

10.65 

7.46 

10.62 

7.50 

10.58 

7.55 

10.55 

7.60 

13 

14 

11.47 

8.03 

11.43 

8.08 

11.40 

8.13 

11.36 

8.18 

14 

15 

12.29 

8.60 

12.25 

8.66 

12.21 

8.71 

12.17 

8.76 

15 

1G 

13.11 

9.18 

13.07 

9.23 

13.03 

9.29 

12.99 

9.35 

16 

17 

13.93 

9.75 

13.88 

9.81 

13.84 

9.87 

13.80 

9.93 

17 

18 

14.74 

10.32 

14.70 

10.39 

14.65 

10.45 

14.61 

10.52 

18 

19 

15.56 

10.90 

15.52 

10.97 

15.47 

11.03 

15.42 

11.10 

19 

20 

16.38 

11.47 

16.33 

11.54 

16.28 

11.61 

18.23 

11.68 

20 

■ 21 

17.20 

12.05 

17.15 

12.12 

17.10 

12.19 

17.04 

12.27 

21 

22 

18.02 

12.62 

17.97 

12.70 

17.91 

12.78 

17.85 

12.85 

22 

23 

18.81 

13.19 

18.78 

13.27 

13.72 

13.36 

18.67 

13.44 

23 

24 

19.66 

13.77 

19.60 

13.85 

19.54 

13.94 

19.48 

14.02 

24 

25 

20.48 

14.34 

20.42 

14.43 

20.35 

14.52 

20.29 

14.61 

25 

26 

21.30 

14.91 

21.23 

15.0’ | 

21.17 

15.10 

21.10 

15.19 

26 

27 

22.12 

15.49 

22.05 

15.58 

21.98 

15.68 : 

i21.91 

15.77 

27 

28 

22.94 

16.06 

22.87 

16.IS 

22.80 

16.26 i 

22.72 

16.36 

28 

29 

23.76 

16.63 

23.68 

16.74 

23.61 

16.84 

; 23.54 

16.94 

29 

30 

24.57 

17.21 

24.50 

17.31 

24.42 

17.42 

!24.35 

17.53 

30 

31 

25.39 

17.78 

25.32 

17.89 

25.24 

18.00 

125.16 

18.11 

31 

32 

26.21 

18.35 

26.13 

18.47 

26.05 

18.58 

25.97 

18.70 

32 

33 

27.03 

18.93 

26.95 

19.05 

26.87 

19.16 

26.78 

19.28 

33 

34 

27.85 

19.50 

27.77 

19.62 

27.68 

19.74 

27.59 

19.86 

34 

35 

28.67 

20.03 

28.58 

20.20 

28.49 

20.32 

28.41 

20.45 

35 

3G 

29.49 

20.65 

29.40 

20.78 

29.31 

20.91 

|29.22 

21.03 

36 

37 

30.31 

21.22 

30.22 

21.35 

30.12 

21.49 

I 30.03 

21.62 

37 

38 

31.13 

21.80 

31.03 

21.93 

30.91 

22.07 

!30.84 

22.20 

38 

39 

31.95 

22.37 

31.85 

22.51 

31.75 

22.65 

31.65 

22.79 

39 

40 

32.77 

22.94 

32.67 

23.09 

32.56 

23.23 

32.46 

OO Q -V 
s* j • O 1 

40 

41 

33.59 

23.52 

33.48 

23.68 

33.3S 

23.81 

33.27 

23.95 

41 

42 

34.40 

24.09 

34.30 

24.24 

34.19 

24.39 

134.09 

24.54 

42 

43 

35.22 

24.66 

35.12 

24.82 

35.01 

24.97 

134.90 

25.12 

43 

44 

36.04 

25.24 

35.93 

25.39 

35.82 

25.55 

! 35.71 

25.71 

44 

45 

36.86 

25.81 

36.75 

25.97 

36.64 

26.13 

j 36.52 

26.29 

45 

46 

37.68 

26.38 

37.57 

26.55 

37.45 

26.71 

37.33 

26.88 

46 

47 

33.50 

26.96 

38.38 

27.13 

38.26 

27.29 

38.14 

27.46 

47 

48 

39.32 

27.53 

39.20 

27.70 

39.08 

27.87 

38.96 

28.04 

48 

49 

40.14 

28.11 

40.02 

28.28 

39.89 

28.45 

39.77 

28.63 

49 

50 

40.96 

28.68 

40.83 

28.86 

40.71 

29 . 04 

|40.5S 

29.21 

50 

d 

o 

£ 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

G 

£ 

d 

+-> 

V) 

5 

55 Deg. 

54f Deg. 

54$ Deg. 

54^ Deg. 

Vi 

5 

























































































TRAVERSE TABLE 


73 


c 

Ji 

t—♦* 

p 

35 Deg. 

35} Deg. 

35£ Deg. 

351 Deg. 

Distanct). 

a 

o 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

.Lat, 

Dep. 

51 

41 .78 

29.25 

41.65 

29.43 

41.52 

29.62 

41.39 

29.80 

51 

52 

42.60 

29.83 

42.47 

30.01 

42.33 

30.20 

42.20 

30.38 

52 

53 

43.42 

30.40 

43.28 

30.59 

43.15 

30.78 

43.01 

30.97 

53 : 

54 

44.23 

30.97 | 

44.10 

31.17 

43.96 

31 .36 

43.82 

31 .55 

54 ' 

55 

45.05 

31.55 

44.92 

31.74 

44.78 

31.94 

44.64 

32.13 

55 

56 

45.87 

32.12 

45.73 

32.32 

45.59 

32.52 

45.45 

32.72 

56 

57 

46.69 

32.69 

46.55 

32.90 

46.40 

33.10 

46,26 

33.30 

57 

58 

47.51 

33.27 

47.37 

33.47 

47.22 

33.68 

47.07 

33.89 

58 

59 

48.33 

33.84 

48.18 

34.05 

48.03 

34.26 

47.88 

34.47 

59 

60 

49.15 

34.41 

49.00 

34.63 

48.85 

34.84 

48.69 

35.05 

60 

61 

49.97 

34.99 

49.82 

35.21 

49.66 

35.42 

49.51 

35.64 

61 

62 

50.79 

35.56 

50.63 

35.78 

50.48 

36.00 

50.32 

36.22 

62 

63 

51.61 

36.14 

51.45 

36.36 

51.29 

36.58 

51.13 

36.81 

63 

64 

52.43 

36.71 

52.27 

36.94 

52.10 

37.16 

51.94 

37.39 

64 

65 

53.24 

37.28 

53.08 

37.51 

52.92 

37.75 

52.75 

37.98 

65 

66 

54.06 

37.86 

53.90 

38.09 

53.73 

38.33 

53.56 

38.56 

66 

67 

54.88 

38.43 

54.71 

38.07 

54.55 

38.91 

54.38 

39.14 

67 

68 

55.70 

39.00 

55.53 

39..25 

55.36 

39.49 

55.19 

39.73 

68 

69 

56.52 

39.58 

56.35 

39.82 

56.17 

40.07 

56.00 

40.31 

69 

70 

57.34 

40.15 

57.16 

40 40 

56.99 

40.65 

56.81 

40.90 

70 

71 

58.16 

40.72 

57.98 

40.98 

157.80 

41.23 

57.62 

41.4S 

71 

72 

58.98 

41.30 

58.80 

41.55 

58.62 

41.81 

58.43 

42.07 

72 

73 

59.80 

41.87 

59.61 

42.13 

59.43 

42.39 

59.24 

42.65 

73 

74 

60.62 

42.44 

60.43 

43.71 

60.24 

42.97 

60.06 

43.23 

74 

75 

61.44 

43.02 

61.25 

43.29 

61.06 

43.55 

60.87 

43.82 

75 

76 

62.26 

43.59 

62.06 

43.86 

61.87 

44.13 

61.68 

44.40 

76 

77 

63.07 

44.17 

62.88 

44.44 

'62.69 

44.71 

62.49 

44.99 

77 

78 

63.89 

44.74 

63.70 

45.02 

63.50 

45.29 

63.30 

45.57 

78 

79 

64.71 

45.31 

64.51 

45.59 

64.32 

4-5.88 

64.11 

46.16 

79 

80 

65.53 

45.89 

65.33 

46.17 

65.13 

46.46 

64.93 

46.74 

80 

81 

66.35 

46.46 

66.15 

46.75 

65.94 

47.04 

65.74 

47.32 

81 

82 

67.17 

47.03 

66.96 

47.33 

66.76 

47.62 

66.55 

47.91 

82 

83 

67.99 

47.61 

67.78 

47.90 

67.57 

48.20 

67.36 

48.49 

83 

84 

6S.81 

48.18 

68.60 

48.48 

68.39 

48.78 

68.17 

49.08 

84 

85 

69.63 

48.75 

69.41 

49.06 

69.20 

49.36 

68.98 

49.66 

85 

86 

70.45 

49.33 

70.23 

49.63 : 

70.01 

49.94 

69.80 

50.25 

86 

87 

71.27 

49.90 

71.05 

50.21 ! 

70.83 

50.52 

70.61 

50.83 

87 

88 

72.09 

50 47 

71.86 

50.79 ; 

71.64 

51.10 ; 

71.42 

51.41 

8S 

89 

72.90 

51.05 

72.68 

51.37 

1 72.46 

51.68 

72.23 

52.00 

89 

90 

73.72 

51.62 

73.50 

51.94 

,73.27 

52.26 i 

73.04 

52.58 

90 

91 

74.54 

52.20 

74.31 

52.52 1 

74.08 

52.84 

73.85 

53.17 

91 

92 

75.36 

52.77 

75.13 

53.10 

74.90 

53.42 

74.66 

53.73 

92 

93 

76.18 

53.34 

75.95 

53.67 ’ 

75.71 

54.01 

75.48 

54.34 

93 

94 

77.00 

53.92 

76.76 

54.25 

76.53 

54.59 

76.29 

54.92 

94 

95 

77.82 

54.49 

77.58 

54.83 I 

77.34 

55.17 

77 10 

55.50 

95 

96 

78.64 

55.06 

78.40 

55.41 ; 

78.16 

55.75 

77.91 

56.09 

96 

97 

79.46 

55.64 

I 79.21 

55.98 

78 97 

56.33 

i78.72 

56.67 

97 

98 

80.28 

56.21 

80.03 

56.56 

79.78 

56.91 

79.53 

57.26 

98 

99 

81.10 

56.78 

80.85 

57.14 

80.60 

57.49 

80.35 

57.84 

99 

J00 

81.92 

57.36 

81.66 

57.71 

SI .41 

58.07 

|81.16 

58.42 

100 

6 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

a 

3 

55 Deg. 

54} Deg. 

54} Deg. 

1 

54} Deg. 


































































































74 


TRAVERSE TABLE 


a 

r~* 

P 

36 Deg. 

36i Deg. 

3S£ 

Deg. 

36] Deg. 

e 
►— • 

u> 

p 

3 

o 

ra 

Lat. 

Dep. 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

D 

O 

CD 

1 

0.31 

0.59 

0.81 

0.59 

0.80 

0.59 

0.80 

0.00 

1 

2 

1 . G2 

1.18 

1.61 

1.18 

1.61 

1.19 

1.60 

1 20 

2 

3 

2.43 

1.76 

2.42 

1.77 

2.41 

1.73 

2.40 

1.79 

3 

4 

3.21 

2.35 

3.23 

2.37 

3.22 

2.33 

3.20 

2.39 

4 

5 

4.05 

2 . 94 

4.03 

2.96 

4.02 

2.97 

4.01 

2.99 

5 

6 

4.85 

3.53 

4.84 

3.55 

4.82 

3.57 

4.81 

3.59 

6 

7 

5.66 

4. i 1 

5.65 

4.14 

5.63 

4.16 

5.61 

4.19 

7 

8 

6.47 

4.70 

6.45 

4.73 

6.43 

4.76 

6.41 

4.79 

8 

a 

7.28 

5.29 

7.26 

5.32 

7.23 

5.35 

7.21 

5 . 3S 

9 

10 

8.09 

5.83 

8.06 

5.91 

8.04 

5.95 

8.01 

5.98 

10 

n 

8.90 

6.47 

8.87 

6.50 

8.84 

6.54 

8.81 

G. 53 

1 ! 

12 

9.71 

7.05 

9.68 

7.10 

9.65 

7.14 

9.61 

7.18 

12 

13 

10.52 

7.64 

10.48 

7.69 

10.45 

7.73 

10.42 

7.78 

13 

14 

11.33 

8.23 

11.29 

8.28 

11.25 

8.33 

11.22 

8.38 

14 

15 

12.14 

8.82 

12.10 

8.87 

! 12.06 

8.92 

12.02 

8.97 

15 

16 

12.94 

9.40 

12.90 

9.46 

12.86 

9.52 

12.82 

9.57 

16 

17 

13.75 

9.99 

13.71 

10.05 

13.67 

10.11 

13.62 

10. 17 

17 

18 

14.56 

10.58 

14.52 

10.04 

14.47 

10.71 

14.42 

10.77 

18 

19 

15.37 

i 11.17 

15.32 

11.23 

15.27 

11.30 i 

15.22 

11.37 

19 

20 

16.18 

11.76 

16.13 

11.83 

16.08 

11.90 

16.03 

11.97 

20 

21 

16.99 

,12.34 

16.94 

12.42 

16.88 

12.49 

16.83 

12.56 

21 

22 

17.80 

12.93 

17.74 

13.01 

17.68 

13.09 

17.63 

13. 16 

22 

23 

18.01 

13.52 

18.55 

13.60 

18.49 

13.68 

18.43 

13.76 

23 

24 

19.42 

14.11 

19.35 

14.19 1 

19.29 

14.28 

19.23 

14.36 

24 

25 

20.23 

14.69 

20.16 

14.78 ! 

20.10 

14.87 

20.03 

14.96 

25 

26 

21 .03 

15.28 

20.97 

15.37 

20.90 

15.47 

20.83 

15.56 

26 

27 

21.81 

15.87 

21.77 

15.97, 

21.70 

16.06 

21.63 

16.15 

27 

28 

22.65 

16.46 

22.53 

1 6.56 

22.51 

16.65 

22.44 

16.75 

28 

29 

23.46 

17.05 

23.39 

17.15 

23.31 

17.25 

23.24 

17.35 

29 

30 

24.27 

17.63 

24.19 

17.74 

24.12 

17.84 

24.04 

17.95 

30 

31 

25.08 

18.22 

25.00 

18.83 

24.92 

18.44 

24.84 

18.55 

31 

32 

25.89 

13.81 

25.81 

18.92 

25.72 

19.03 

25.64 

19.15 

32 

33 

26.70 

19.40 

26.61 

19.51 

26.53 

19.63 

26.44 

19.74 

33 

34 

27.51 

19.98 

27.42 

20.10 

27.33 

20.22 

27.24 

20.34 

34 

35 

28.32 

20.57 

28.23 

20.70 

28.13 

20.82 

28.04 

20.94 

35 

36 

29.12 

21.16 

29.03 

21 .29 

28.94 

21.41 

23.85 

21.54 

36 

37 

29.93 

21.75 

29.84 

21.88 

29.74 

22.01 

29.65 

22.14 

37 

38 

30.74 

22.34 

30.64 

22.47 

30.55 

22.60 

30.45 

22.74 

33 

39 

31.55 

22.92 

31.45 

23.06 

31.35 

23.20 

31 .25 

23.33 

39 

40 

32.36 

23.51 

32.26 

23.65 

32.15 

23.79 

32.05 

23.93 

40 

41 

33.17 

24.10 

33.06 

24.24 

32.96 

24.39 

32.85 

24.53 

41 

42 

33.98 

24.69 

33.87 

24.83 

33.76 

24.93 

33.65 

25.13 

42 

43 

34.79 

25.27 

34.68 

25.43 

34.57 

25.58 

34.45 

25.73 

43 

44 

35 . 60 

25.86 

35.48 

26 . 02 

35.37 

26.17 

35.26 

26.33 

44 

45 

30.41 

26.45 

36.29 

26.61 

36.17 

26.77 

36.06 ! 

26.92 

45 

46 

37.21 

27.04 

37.10 

27.20 

36.98 

27.36 

36.86 

27 . 52 

46 

47 

38.02 

27.63 

37.90 

27.79 

37.78 

27 . 96 

37.66 j 

28.12 

47 

48 

38.83 

28 . 21 

38.71 

28 . 3.8 

38.59 

28.55 

38.46 1 

28.72 

48 

49 

39.64 

28.80 

39.52 

28.97 

39.39 

29.15 

39.26 

29.32 

49 

60 

40.45 

29.39 

40.32 

29.57 

40.19 

29.74 

40.06 

29.92 

50 

oi 

^ i 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dcp. 

Lat. 

0) 

o 

G 

a 

-t—> i 

in 

i 5 

54 Deg. 

o 

53] Dog. 

53} Deg. 

53] Deg. 

d 

(U 

• H 

Q 
















































































































TRAVERSE TAELE. 


75 


o 

• 

r-» 

P 

36 Deg. 

36} Deg. 

36} Deg. 

363 Deg. 

i 

O 

• 

7 

r*- 

3 

O 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep 

Lat. 

Dep. 

O 

61 

41.26 

29.98 

41.13 

30.16 

41.00 

30.34 

40.86 

:30.51 

~51 

52 

142.07 

30.56 

41.94 

30.75 

41.80 

30.93 

41.67 

31.11 

52 

53 

142.88 

31.15 

42.74 

31.34 

142.60 

31.53 

42.47 

31 .71 

53 

54 

43.69 i31.74 

43.55 

31.93 

43.41 

32.12 

43.27 

32.31 

54 

55 

44.50 

32.33 

44.35 

32.52 

44.21 

32.72 

44.07 

32.91 

55 

56 

45.30 

32.92 

45.16 

33. 11 

45.02 

33.31 

44.87 

33.51 

56 

57 

46.11 

33.50 

45.97 

33.70 

;45.82 

33.90 

45.67 

34.10 

57 

58 

46.92 

134.09 

46.77 

34.30 

46.62 

34.50 

46.47 

34.70 

5S 

59 

47.73 

34.68 

47.58 

34.89 

47.43 

35 09 

47.27 

3& 30 

59 

60 

48.54 

35.27 

48.39 

35.48 

|48.23 

35.69 

48.08 

35.90 

60 

61 

49.35 

35.85 

49.19 

36.07 

]49.04 

36.28 

48.88 

36.50 

61 

62 

50.16 

|36.44 

50.00 

36.66 

49.84 

36.88 

49.68 

37.10 

62 

63 

■50.97 

37.03 

50.31 

37.25 

!50.64 

37.47 

50.48 

37.69 

63 

64 

51.78 

37.62 

51.61 

37.84 

51 .45 

38.07 

51 .28 

38.29 

64 

65 

52.59 

38,21 

52.42 

38.44 

52.25 

38.66 

52.08 

3S.89 

65 

66 

53.40 

38.79 

53.23 

39.03 

153.05 

39.26 

52.88 

39.49 

GO 

67 

54.20 

39.38 

54.03 

39.62 

j 53.86 

39.85 

53.68 

40.09 

67 

68 

55.01 

39.97 

54.84 

40.21 

54.66 

40.45 

54.49 

40.69 

68 

69 

55.82 

40.56 

55.64 

40. SO 

55.47 

41.04 ; 

55.29 

4 1.23 

69 

70 

56.63 

41.14 

56.45 

41.39 

!56.27 

41.64 | 

56.09 

41.88 

70 

71 

57.44 

41.73 

57.26 

41.98 

57.07 

42.23 | 

56.89 

42.48 

71 

72 

58.25 

42.32 

58.06 

42.57 

57.88 

42.83 

57.69 

43.08 

72 

73 

59.06 

42.91 

58.87 

43.17 

58.68 

43.42 

58.49 

43.68 

73 

74 

59.87 

43.50 

59.68 

43.76 

59.49 

44.02 

59.29 

44.28 

74 

75 

60.68 

44.08 

60.4S 

44.35 

60.29 

44.61 

60.09 

44.87 

75 

76 

61.49 

44.67 

61.29 

44.94 

61.09 

45.21 

60.90 

45.47 

76 

77 

62.29 

45.26 

62.10 

45.53 

61.90 

45.80 

61.70 

45.07 

77 

78 

63. 10 

45.85 

62.90 

46.12 

62.70 

46.40 

|62.50 

46,07 

78 

79 

63.91 

46.43 

63.71 

46.71 

63.50 

46.99 

63.30 

47.27 

79 

80 

64.72 

47.02 

64.52 

47.30 

64.31 

47.59 

j 64.10 

47.87 

80 

81 

65.53 

47.61 

65.32 

47.90 

65.11 

48.18 

64.90 

48.46 

81 

82 

66.34 

48.20 

66.13 

48.49 

!65.92 

48.78 

65.70 

49.06 

82 

83 

67.15 

48.79 

66.93 

49.08 

j 06.72 

49.37 

66.50 

49.66 

83 

84 

67.96 | 

49.37 

67.74 

49.67 

67.52 

49.97 

67.31 

50.26 

84 

85 

68.77 

49.96 

68.55 

50.26 

68.33 

50.56 

68.11 

50.86 

85 

86 

69.58 

50.55 

69.35 

50.85 

69.13 

51.15 

68.91 

51.46 

86 

87 

70.38 

51.14 

70.16 

51.44 

69.94 

51.75 

69.71 

52.05 

87 

88 

71.19 ! 

51.73 

70.97 

52.04 

70.74 

52.34 

70.51 

52.65 

88 

89 

72.00 

52.31 

71.77 

52.63 

71.54 

52.94 

71.31 

53.25 

89 

90 

72.81 j 

52.90 

72.58 

53.22 

72.35 

53.53 

72.11 

53.85 

90 

91 

73.62 1 

53.49 

73.39 

53.81 

73.15 

54.13 

72.91 

54.45 

91 

92 

74.43 

54.03 ! 

74.19 

54.40 

73.95 

54.72 

73.72 

55.05 

92 

93 

75.24 1 

54.66 

75.00 

54.99 

74.76 

55.32 

74.52 

55.64 

93 

94 

76.05 

55.25 

75.81 

55.58 

75.56 

55.91 

nr. oo 

1 *) • 

56.24 

94 

95 

76.86 

55.84 

76.61 

56.17 

76.37 

56.51 

76.12 

56.84 

95 

96 

77.67 

56.43 

77.42 

56.77 

77.17 

57.10 

76.92 

57.44 

96 

97 

78.47 

57.02 

78.23 

57.36 

77.97 

57.70 

77.72 

58.04 

97 

93 

79.28 

57.60 

79.03 

57.95 1 

78.78 

58.29 

78.52 

58.64 

98 

99 

80.09 

58.19 

79.84 

58.54 

79.58 

58.89 

79- 32 

59.23 

93 

ioo; 

80.90 : 

58.78 

80.64 

59.13 

80.39 

59.48 

80.13 

59.83 

11)0 

6 

u 

~ 1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep 

Lat. 

Distance. 

w i 

i 5 ' 

54 Deg. 

531 Deg - . 

53} Deg. 

53} Deg. 









































































































76 


TRAVERSE TABLE. 


a 

% 

37 Deg. 

37± Deg. 

37£ Deg. 

37! Deg. 

e 

m 

n*- 

p 

3 

O 

CE 

Lat. 

Dcp. 

Lat. I 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

re 

“ 1 

0.80 

0.60 

0.80 

0.61 

0.79 

0.61 

0.79 

0.61 

1 

o 

1.60 

1.20 

1.59 

1.21 

1.59 

1.22 

1.58 

1.22 

2 

3 

2.40 

1.81 

2.39 

1.82 

2.38 

] .83 

2.37 

1.84 

3 

4 

3.19 

2.41 

3.18 

2.42 

3.17 

2.43 

3.16 

2.45 

4 

5 

3.99 

3.01 

3.98 

3.03 

3.97 

3.04 

3.95 

3.00 

5 

6 

4.79 

3.61 

4.78 

3.63 | 

4.76 

3.65 

4.74 

3.67 | 

6 

t 

5.59 

4.21 

5.57 

4.24 | 

5.55 

4.26 

5.53 

4.29 j 

7 

8 

6.39 

4.81 

6.37 

4.84 

6.35 

4.87 

6.33 

4.90 

8 

9 

7.19 

5.42 

7.16 

5 45 

7.14 

5.48 

7.12 

5.51 

9 

10 

7.99 

6.02 

7.96 

6.05 | 

7.93 

6.09 

7.91 

6.12 

10 

11 

8.78 

6.62 

8.76 

6.66 1 

8.73 

6.70 

8.70 

6.73 

11 

12 

9.58 

7.22 

9.55 

7.26 i 

9.52 

7.31 

9.49 

7.35 

12 

13 

10.33 

7.82 

10.35 

7.87 

10.31 

7.91 

10.28 

7.96 

13 

14 

11.18 

8.43 

11.14 

8.47 

11.11 

8.52 

11.07 

8.57 

14 

15 

11.98 

9.03 

11.94 

9.08 

11.90 

9.13 

11.86 

9.18 

15 

16 

12.78 

9.63 

12.74 

9.68 

12.69 

9.74 

12.65 

9.80 

16 

17 

13.58 

10.23 

13.53 

10.29 

13.49 

10.35 

13.44 

10.41 

17 

18 

14.38 

10.83 

14.33 

10.90 

14.28 

10.96 

14.23 

11.02 

18 

19 

15.17 

11.43 

15.12 

11.50 

15.07 

11.57 

15.02 

11.63 

19 

20 

15.97 

12.04 | 

15.92 

12.11 

15.87 

12.18 

15.81 

12.24 

20 

21 

16.77 

12.64 

16.72 

12.71 

16.66 

12.78 

16.60 

12.86 

21 

22 

17.57 

13.24 

17.51 

13.32 

17.45 

13.39 

17.40 

13.47 

22 

23 

18.37 

13.84 

18.31 

13.92 

13.25 

14.00 

18.19 

14.08 

23 

24 

19.17 

14.44| 

19.10 

14.53 

19.04 

14.61 

18.98 

14.69 

24 

25 

19.97 

15.05 

19.90 

15.13 

19.83 

15.22 

19.77 

15.31 

25 

26 

20.76 

15.65 

20.70 

15.74 

20.63 

15.83 

20.56 

15.92 

26 

27 

21.56 

16.25 

21.43 

16.34 

21.42 

16.44 

21.35 

16.53 

27 

28 

22.36 

16.85 

22.29 

16.95 

22.21 

17.05 

22.14 

17.14 

2S 

29 

23.16 

17.45 

23.03 

17.55 

23.01 

17.65 

22.93 

17.75 

29 

30 

23.96 

18.05 

23.88 

18.16 

23.80 

18.26 

23.72 

18.37 

30 

31 

24.76 

18.66 

24.68 

18.76 

24.59 

18.87 

24.51 

18.98 

31 

32 

25.56 

19.28 

25.47 

19.37 

25.39 

19.48 

25.30 

19.59 

32 

33 

26.35 

19.86 

26.27 

19.97 

26.18 

20.09 

26.09 

20.20 

33 

34 

27.15 

20.46 

27.06 

20.58 

26.97 

20.70 

26.88 

20.82 

34 

35 

27.95 

21.06 

27.86 

21.19 

27.77 

21.31 

27.67 

21.43 

35 

36 

.28.75 

21.67 

28.66 

21.79 

28.56 

21.92 

28.46 

22.04 

36 

37 

29.55 

22.27 

29.45 

22.40 

29.35 

22.52 

29.26 

22.65 

37 

38 

30.35 

22.87 

30.25 

23.00 

30.15 

23.13 

30.05 

23.26 

33 

39 

31.15 

23.47 

31.04 

23.61 

30.94 

23.74 

30.84 

23.83 

39 

40 

31.95 

24.07 

31.84 

24.21 

31.73 

24.35 

31.63 

24.49 

40 

41 

32.74 

24.67 

32.64 

24.82 

32 53 

24.96 

32.42 

25.10 

41 

42 

33.54 

25.28 

33.43 

25.42 

33 32 

25.57 

33.21 

25.71 

42 

43 

34.34 

25.88 

34.23 

26.03 

34.11 

26.18 

34.00 

26.33 

43 

44 

35.14 

20.48 

35.02 

26.63 

34.91 

26.79 

34.79 

26.94 

i 44 

45 

35.94 

27.08 

35.82 

27.24 

35.70 

27.39 

35.58 

! 27.55 

45 

46 

36.74 

27.68 

36.62 

27.84 

36.49 

28.00 

36.37 

S 28.16 

1 46 

47 

37.54 

28.29 

37.41 

28.45 

37.29 

1 28.61 

37.16 

28.77 

- 47 

48 

38.33 

28.89 

38.21 

29.05 

38.03 

! 29.22 

37.95 

29.39 

48 

49 

39.13 

29.49 

39.00 

29.66 

33.87 

29.83 

38.74 

30.00 

49 

50 

39.93 

30.09 

39.80 

30.26 

39.67 

30.44 

39.53 

30.61 

50 

d 

o 

S3 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

id 

»-) 

JO 

H 

53 Deg. 

52| Deg. 

52% I)eg. 

52| Deg. 

cd 

C 0 

• ~4 

Q 
































































































































Distance.I O CD CD CD CD CD CD CD CD CD CDOOCDOOOOOOOOQOOOOO C»<!<J<5<5<J<J<!^?^|<JCT5CniOiOC500Cia5|C5CiOTtnO’DitntnOTm •o'mTnQT/'T 

I OOOO^DOit?.«Mr- OCOOO^JO enroots*— OCDCC<lC5iLn^J0M^|OCD00-vl05Cnrfi.CDt5H-|ocDa0*-}C5 0T|^a»iCi'— !U. 


TRAVERSE TABLE. 


77 


37 Deg. 

37* Deg. 

37^ Deg. 

371 Deg. 

o 
»— • 

Ul 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

I 

—> 

O 

CD 

40 

.73 

30. 

69 

40.60 

30.87 

40 

.46 

31. 

05 

40. 

33 

31 

22 i 

51 

41 

.53 

31. 

29 

41.39 

31.48 

41 

.25 

31. 

66 

41. 

12 

31. 

84 

52 

42 

.33 

31. 

90 

42.19 

32.08 

42 

.05 

32. 

26 

41. 

91 

32. 

45 

53 

43 

.13 

32. 

50 

42.98 

32.69 

42 

.84 

32. 

87 

42. 

70 

33. 

06 

54 

43 

.92 

33. 

10 

43.78 

33.29 

43 

.63 

33. 

48 

43. 

49 

33. 

67 

55 

44 

.72 

33. 

70 

44.58 

33.90 

44 

.43 

34. 

CO 

44. 

28 

34. 

28 

56 

45 

. 52 

34. 

30 

45.37 

34.50 

45 

.22 

34. 

70 

45. 

07 

34. 

90 

57 

46 

.32 

34. 

91 

46.17 

35.11 

46 

.01 

35. 

31 

45. 

86 

35. 

51 

58 

47 

. 12" 

35. 

51 

46.96 

35.71 

46 

.81 

35. 

92 

46. 

65 

36. 

12- 

59 

47 

.92 

36. 

11 

47.76 

36.32 

47 

.60 

36. 

53 

47. 

44 

36. 

73 

60 

48 

.72 

36. 

71 

48.56 

36.92 

48 

.39 

37. 

13 

48. 

23 

37. 

35 

61 

49 

.52 

37. 

31 

49.35 

37.53 

49 

.19 

37. 

74 

49. 

02 

37. 

96 

62 

'50 

.31 

37. 

91 

50.15 

38.13 

49 

.98 

38. 

35 

49. 

81 

38. 

57 

63 

51 

.11 

38. 

52 

50.94 

38.74 

50 

.77 

38. 

96 

50. 

60 

39. 

18 

64 

51 

.91 

39. 

12 

51.74 

39.34 

51 

.57 

39. 

57 

51. 

39 

39. 

79 

65 

52 

.71 

39. 

72 

52.54 

39.95 

52 

.36 

40. 

18 

52. 

19 

40. 

41 

66 

53 

.51 

40. 

32 

53.33 

40.55 

53 

.15 

40. 

79 

52. 

98 

41. 

02 

67 

54 

.31 

40. 

92 

54.13 

41.16 

53 

.95 

41. 

40 

53. 

77 

41. 

63 

68 

55 

.11 

41. 

53 

54.92 

41.77 

54 

.74 

42. 

00 

54. 

56 

42. 

24 

69 

65 

.90 

42. 

13 

55.72 

42.37 

55 

.53 

42. 

61 

55. 

35 

42 

86 

70 

56 

.70 

42. 

73 

56.52 

42.98 

56 

.33 

43. 

22 

56. 

14 

43. 

47 

71 

57 

.50 

43. 

33 

57.31 

43.58 

57 

.12 

43. 

83 

56. 

93 

44. 

08 

72 

58 

.30 

43. 

93 

58.11 

44.19 

57 

.91 

44. 

44 

57. 

72 

44. 

69 

73 

59 

.10 

44. 

53 

58.90 

44.79 

58 

.71 

45. 

05 

58. 

51 

45. 

30 

74 

59 

.90 

45. 

14 

59.70 

45.40 

59 

.50 

45. 

66 

59. 

30 

45 

92 

75 

GO 

.70 

45. 

74 

60.50 

46.00 

60 

.29 

46. 

27 

60. 

09 

46 

53 

76 

61 

.49 

46. 

34 

61.29 

46.61 

61 

.09 

46. 

87 

60. 

88 

47 

14 

77 

62 

.29 

46. 

94 

62.09 

47.21 

6l 

.88 

47. 

48 

61. 

67 

47 

75 

78 

63 

.09 

47. 

54 

62.88 

47.82 

62 

.67 

48. 

09 

62. 

46 

48 

37 

79 

63 

.89 

48. 

15 

63.6S 

48.42 

63 

.47 

48 

70 

63 

20 

48 

98 

80 

64 

.89 

48. 

75 

64.48 

49.03 

64 

.26 

49 

31 

64 

05 

49 

.59 

81 

65 

.49 

49. 

35 

65.27 

49.63 

65 

.05 

49 

92 

64 

84 

50 

.20 

82 

66 

.29 

49. 

95 

66.07 

50.24 

65 

.85 

50 

53 

65 

63 

50 

.81 

83 

67 

.09 

50. 

55 

66.86 

50.84 

66 

.64 

51 

14 

66 

42 

51 

.43 

84 

67 

.88 

51. 

15 

67.66 

51.45 

67 

.43 

51 

74 

67 

21 

52 

.04 

85 

68 

.68 

51. 

76 

68.46 

52.06 

68 

.23 

52 

35 

68 

00 

52 

.65 

86 

69 

.48 

52. 

36 

69.25 

52.66 

69 

.02 

52 

96 

68 

79 

53 

.26 

87 

70 

.28 

52. 

96 

70.05 

53.27 

69 

.82 

53 

.57 

69 

58 

53 

.88 

88 

71 

.08 

53. 

56 

70.84 

53.87 

70 

.61 

54 

.18 

70 

.37 

54 

.49 

89 

71 

.88 

54. 

16 

71.64 

54.48 

71 

.40 

54 

.79 

71 

16 

55 

.10 

90 

72 

.68 

54. 

77 

72.44 

55.08 

72 

.20 

55 

.40 

71 

.95 

55 

.71 

91 

73 

.47 

55. 

37 

73.23 

55.69 

72 

.99 

56 

.01 

72 

.74 

56 

.32 

92 

74 

.27 

55. 

97 

74.03 

56.29 

73 

.78 

56 

.61 

73 

.53 

56 

.94 

93 

75 

.07 

56. 

a 7 

74.82 

56.90 

74 

.58 

57 

.22 

74 

.32 

57 

.55 

94 

75 

.87 

57. 

17 

75.62 

57.50 

75 

.37 

57 

.83 

75 

.12 

58 

. 16 

95 

76 

.67 

57. 

77 

76.42 

58.11 

76 

.16 

58 

.44 

75 

.91 

58 

.77 

96 

77 

.47 

58. 

38 

77.21 

58.71 

76 

.96 

59 

.05 

76 

.70 

59 

.39 

97 

78 

.27 

58 

98 

78.01 

59.32 

77 

.75 

59 

.66 

! 77 

.49 

60 

.00 

98 

79 

.06 

59. 

58 

78.80 

I 59.92 

78 

. 54 

60 

.27 

78 

.28 

60 

.61 

99 

79 

.86 

60. 

18 

79.60 

j 60.53 

79 

.34 

60 

.88 

1 79 

.07 

1 ci 

.22 

100 

Dcp. 

L it t. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

d 

u 

G 

53 Deg. 

52f Deg. 

1 

52* Deg. 

i 

1 

52} 

De 

S- 

♦J 

Ifi 

I Q 
























































































78 


TRAVERSE TABLE 


►—* 

w 

zn ’ 

r-*- 


38 Dog. 

| 

38} Deg. 

38} Deg 


CO 

GO 

Deg. 

5 

rr.' 

<-*■ 

c: 

;3 

n 

p 

L 

It. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dup. 

y 

n 

ct 

I 

0. 

79 

0. 

62 

0.79 

0.62 

0.78 

0. 

62 

0. 

78 

0. 

63 

i 

2 

1 

58 1 

1. 

23 

1.57 

1.24 

1.57 

1. 

24 

1. 

56 

1. 

25 

€> 

3 

<> 

36 1 

1 . 

85 

2.36 

1.86 

2.35 

1. 

87 

2. 

34 

1. 

88 

3 

4 

3. 

15 j 

9 

/w • 

46 

3.14 

2.48 

3.13 

2. 

49 

3. 

12 

2. 

50 

4 

5 

3 

94 ! 

3. 

08 

3.93 

3.10 

3.91 

3 

11 

3. 

90 

3. 

13 

5 

G 

4 

73 

3. 

69 

4.71 

3.71 

4.70 

3. 

74 

4. 

68 

3. 

76 

3 

7 

5 

52 

4. 

31 

5.50 

4.33 

5.48 

4. 

36 

5. 

46 

4. 

38 

7 

8 

6 

30 

4. 

93 

6.28 

4.95 

6.26 

4. 

98 

6. 

24 

5. 

01 

8 

9 

r** 

> / 

09 

5. 

54 

7.07 

5.57 

7.04 

5. 

60 T 

7. 

02 

5. 

63 

9 

10 

7 

88 

6. 

16 

7.85 

6.19 

7.83 

6. 

23 

7. 

80 

6. 

26 

10 

11 

8 

67 

6. 

77 

8.64 

6.81 

8.61 

6. 

85 

8. 

53 

6. 

39 

11 

12 

9 

46 

7. 

39 

9.42 

7.43 

9.39 

7. 

47 

9. 

36 

i . 

51 

12 

13 

10 

24 

8. 

00 

10.21 

8.05 

10.17 

8. 

09 

10 

14 

8. 

14 

13 

14 

11 

03 

8. 

62 

10.99 

8.67 

10.96 

8. 

72 

10 

92 

8. 

76 

14 

15 

11 

.82 

9. 

23 

11.78 

9.29 

11.74 

9. 

34 

11 

70 

9. 

39 

15 

16 

12 

61 

9. 

85 

12.57 

9.91 

12.52 

9. 

96 

12 

48 

10. 

01 

16 

17 

13 

40 

10. 

47 

13.35 

10.52 

13.30 

10. 

58 

13 

26 

10. 

64 

17 

18 

14 

.18 

11. 

08 

14.14 

11.14 

14.09 

11. 

21 

14 

04 

11. 

27 

18 

. 19 

14 

97 

1 1. 

70 

14.92 

11.76 

14.87 

11 

83 

14 

82 

11. 

89 

19 

20 

15 

.76 

12. 

31 

15.71 

12.38 

15.65 

12. 

45 

15 

.60 

12. 

52 

20 

21 

16 

55 

12. 

93 

16.49 

13.00 

16.43 

13. 

07 

16 

.33 

13. 

14 

21 

22 

17 

.34 

13. 

54 

17.2S 

13.62 

17.22 

13. 

70 

17 

.16 

13 

77 

-v 

23 

18 

12 

14. 

16 

18.06 

14.24 

18.00 

14. 

32 

17 

.94 

14. 

40 

23 

24 

18 

.91 

14. 

78 

18.85 

14.86 

18.78 

14 

94 | 

18 

.72 

15. 

02 

24 

25 

19 

.70 

15 

39 

19 . 63 

15.48 

19.57 

15 

56 i 

19 

.50 

15. 

65 

25 

26 

20 

.49 

16 

01 

20.42 

16.10 

20.35 

16 

19 | 

20 

.23 

16. 

27 

26 

27 

21 

.23 

16 

62 

21.20 

16.72 

21.13 

16 

8] 

1 21 

.06 

16. 

90 

27 

23 

22 

.06 

17 

24 

21.99 

17.33 

21.91 

17 

43 | 

! 21 

.84 

17 

53 

28 

29 

OO 

.85 

17 

S5 

22.77 

17.95; 

22.70 

18 

05 ! 

1 22 

.62 

18 

15 

29 

30 

23 

.64 

18 

47 

23.56 

18.571 

23.48 

18 

63 

; 23 

.40 

18 

78 

30 

31 

24 

.43 

19 

09 

24.34 

19.19 

24.26 

19 

30 

1 24 

.13 

19 

40 

31 

32 

25 

.22 

19 

70 

25.13 

19.81 

25.04 

19 

92 

! 24 

.96 

20 

0.8 

82 

33 

26 

.00 

20 

32 

25.92 

20.43 

25.83 

20 

.54 

25 

.74 

20 

66 

33 

34 

26 

.79 

20 

.93 

26.70 

21.05 

26.61 

21 

17 

26 

• • l.v 

21 

28 

34 

35 

27 

.53 

21 

.55 

27.49 

21.67 

27.39 

21 

79 

! 27 

.30 

21 

91 

35 

36 

28 

.37 

22 

.16 

28.27 

22.29 

28.17 

22 

.41 

28 

.03 

22 

53 

36 

37 

29 

. 16 

22 

78 

29.06 

22.91 

28.96 

23 

.03 

28 

.86 

23 

16 

37 

38 

29 

.94 

23 

.40 

29.84 

23.53 

29.74 

23 

66 

29 

.64 

23 

79 

38 

39 

30 

.73 

24 

.01 

30.63 

24.14 

30.52 

24 

.28 

30 

.42 

24 

41 

39 

40 

31 

. 52 

24 

.63 

31.41 

24.76 

31.30 

24 

.90 

,31 

.2U 

25 

.04 

40 

41 

32 

.31 

25 

.24 

32.20 

25.38 

32.09 

25 

.52 

31 

.98 

25 

66 

r 41 

42 

33 

.10 

25 

.86 

32.98 

26.00 

32.87 

26 

.15 

32 

.76 

26 

.29 

i 42 

43 

33 

.88 

26 

.47 

33.77 

26.62 

33.65 

26 

.77 

33 

.53 

26 

.91 

43 

44 

34 

.67 

27 

.09 

34.55 

27.24 

34.4? 

27 

.39 

34 

.31 

27 

.54 

44 

45 

35 

.46 

27 

.70 

35.34 

27.86 

35.22 

28 

.01 

35 

.69 

28 

.17 

45 

46 

36 

.25 

28 

.32 

36.12 

28.4S 

36.00 

28 

.64 

35 

.87 

28 

79 

45 

47 

37 

.04 

23 

.94 

36.91 

29.10 

36.78 

29 

.26 

36 

. 65 

29 

.42 

47 

48 

37 

.82 

29 

.55 

37.70 

29.72 

37.57 

eo 

/m u 

.88 

37 

.43 

30 

.04 

48 

49 

38 

.61 

30 

.17 

38.48 

30.34 

38.35 

30 

.50 

38 

.21 

30 

.87 

i 49 

50 

39 

.40 

30 

.78 

39.27 

30.95 

39.13 

31 

13 

i 38 

.99 

31 

.30 

, 50 

6 

u 

c 

Dep. 

Lat. 

Dep. 

Lett* 

Dep. 

L 

at. 

1 Dee. 

‘ 

L 

at. 

.r 

] g 

d 

w 

3 

52 Deg. 

i ° 

1 

511 Deg. 

51} Deg. 


51} 

Deg. 

i d i 

! 7 

1 o 

1 



























































































































TRAVERSE TABLE 


79 


o 

38 Deg. 

33} Deg. 

38} Deg. 

381 Deg. 

! O 

i S’ 

w 

o 

CD 

Lat. 

Dep. 

Lat. 

1 

! Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

O 

51 

40.19 

31.40 

| 40.05 

31.57 

39.91 

31.75 

39.77 

31 .92 

51 

52 

40.98 

32.01 

40.84 

32.19 

40.70 

32.37 

40.55 

32.55 

1 52 

53 

41.76 

32.63 

41.62 

32.81 

41.43 

32.99 

41.33 

33. i 7. 

I 53 

54 

42.55 

33.25 

42.41 

33.43 

42.26 

33.62 

42.11 

33.82 

54 

55 

43.34 

33.86 

43.19 

34.05 

43.04 

34.24 

42.89 

34.43 

55 

56 

44.13 

34.48 

43.98 

34.67 

43.83 

34.86 

43.67 

35.05 

1 56 

5 ( 

44.92 

35.09 

44.76 

35.29 

44.61 

35.48 

44.45 

35.63 

57 

58 

45.70 

35.71 

45.55 

35.91 

45.39 

36.11 

45.23 

36.30 

1 58 

59 

45.49 

36.32 

46.33 

36.53 

46.17 

36.73 

46.01 

36.93 

| 59 

60 

47.28 

36.94 

47.12 

37.15 

46.96 

37.35 

46.79 

37.56 

I 60 

61 

48.07 

37.56 

47.90 

37.76 

47.74 

37.97 

47.57 

38. 18 

1 01 

62 

48.86 

3S.17 

•48.69 

38.38 

48.52 

38.60 

43.35 

38.81 

62 

63 

49.64 

38.79 

49.47 

39.00 

49.30 

39.22 

49.13 

39.43 

63 

64 

50.43 

39.40 

50.26 

39.62 

50.09 

39.84 

49.91 

40.06 

64 

65 

51.22 

40.02 

51.05 

40.24 

50.87 

40.46 

50.69 

40.68 

65 

66 

52.01 

40.63 

51.83 

40.86 

51.65 

41.09 

51.47 

41 .3 J 

66 

67 

52.80 

41.25 

52.62 

41.48 

52.43 

41.71 

52.25 

41.94 

67 

68 

53.58 

41.86 

53.40 

42.10 

53.22 

42.33 

53.03 

42.56 

68 

69 

54.37 

42.48 

54.19 

42.72 

54.00 

42.95 

53.81 

43.19 

69 

70 

55.16 

43.10 

54.97 

43.34 

54.78 

43.59 

54.59 

43.81 

70 

71 

55.95 

43.71 

55.76 

43.96 

55.57 

44.20 

55.37 

44 44 

71 

72 

56.74 

44.33 

56.54 

44.57 

56.35 

44.82 

56. 15 

45 07 

72 

73 

57.52 

44.94 

57.33 

45.19 

57.13 

45.44 

j 56.93 

45.89 

73 

74 

58.31 

45.56 

58.11 

45.81 

57 . 91 

46.07 

57.71 

46.32 

74 

75 

59.10 

40.17 

58.90 

46.43 

58.70 

46.89 

58.49 

46.94 

75 

76 

59.89 

46.79 

59 . 68 

47.05 

59.43 

47.31 

59.27 

47.57 

76 

77 

60.68 

47.41 

60.47 

47.67 

60.26 

47.93 

60 05 

48.20 

77 

/8 

61.46 

48.02 

61.25 

48.29 

61.04 

48.56 

60 83 

48.82 

73 

79 

62.25 

48.64 

62.04 

48.91 1 

61.83 

49.18 

61 .61 

49.45 

79 

80 

63.04 

49.25 

62.83 

49.53 i 

62.61 

49.80 

62.39 

50.07 

80 

81 

63.83 

49.87 

63.61 

50.15 

63.39 

50.42 

63.17 

50.70 

81 

82 

64.62 

50.48 

64.40 

50.77 

64.17 

51.05 

63.95 

51.33 

82 

83 

65.40 

51.10 

65.18 

51.33 

64.96 

51.67 

64.73 

51.95 

83 

34 

66.19 

51.72 

65.97 

52.00 : 

65.74 

52.29 

65.51 

52.58 

84 

85 

60.93 

52.33 

66.75 

52.62 1 

66.52 

52.91 

66.29 

53.20 

85 

36 

67.77 

52.95 

67.54 

53.24 

67.30 

53.54 

67.07 

53.83 

86 

87 

68.56 

53.56 

68.32 

53.86 

68.09 

54.16 

67.85 

54.46 

87 

83 

69.34 

54.18 

69.11 

54.48 

68.87 

54.78 

68.63 

55.03 

83 

89 1 

70.13 

54.79 

69.89 

55.10 

69.65 

55.40 

69.41 

55.71 

89 

90 

70.92 

55.41 

70.63 

55.72 

70.43 

56.03 

70.19 

56.33 | 

90 

91 

71.71 

56.03 

71.46 

56.34 

71.22 

56.65 

70.97 

£6.96 

91 

92 

72.50 

56.64 

72.25 

56.96 

72.00 

57.27 

71.75 

5 1 .53 

92 

93 

73. ;s 

57.26 

73.03 

57.58 

72.78 

57.89' 

72.53 

53.21 

93 

94 

74.07 

57.87 

73.82 

58.19 

73.57 

58.52 

73.31 

53.84 I 

94 

95 

74 .86 

58.49 | 

74.61 1 

58.31 

74.35 

59.14 

74.09 

50.46 

95 

96 

75.65 

59.10 

75.39 

59.43 

75.13 

59.76 

74.87 

60 09 

96 

97 

76.44 

59.72 

76.18 

60.05 

75.91 

60.38 

75.65 

60 71 

97 

98 

77.22 

60.33 | 

76.96 

60.67 

76.70 

61.01 

76.43 

61 - 34 

98 

99 

78.01 

60.95 ; 

77.75 

61.29 

77.48 

61.63 

77.21 

81.97 

99 

100 

73.80 

61.571 

78.53 

61.91 | 

78.26 

62.25 

77.99 

62.59 

100 

• 1 

a 

G 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

o 

o 

c 

cd 

72 

• 1 

a 

4 

52 Deg. 

5 If Deg. 

51} Deg. 

51} Deg. 

cd 

</. 

i-h 

































































































































80 


TRAVERSE TABLE. 


o 

*— » 
U2 

39 Deg. 

39.1 Deg. 

39 h 

Deg. 

39.f Deg. 

Dista 

ts 

n 

a 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

a 


0.78 

0.63 

0.77 

0.63 

0.77 

0.64 

0.77 

0.64 

J 

2 

1.55 

' 1.26 

1.55 

1.27 

1.54 

1.27 

1.54 

1.28 

o 

At 

3 

2.33 

1.89 

2.32 

1.90 

2.31 

1.91 

2.31 

1.92 

3 

4 

3.11 

2.52 

3.10 

2.53 

3.09 

2.54 

3.08 

2.56 

4 

5 

3.89 

3.15 

3.87 

3.16 

3.86 

3.18 

3.84 

3.20 

5 

6 

4.60 

3.78 

4.65 

3.80 

! 4.63 

3.82 

4.61 

3.84 

6 

7 

5.44 

4.41 

5.42 

4.43 

| 5.40 

4.45 

5.38 

4.48 

7 

8 

6.22 

5.03 

0.20 

5 . 00 

6.17 

5.09 

6.15 

5.12 

8 

9 

6.99 

5.66 

6.97 

5.69 

1 6.94 

5.72 

6.92 

5.75 

9 

10 

| 7.77 

1 6.29 

7.74 

6.33 

7.72 

6.36 

7.69 

6.39 

10 

li 

| 8.55 

6.92 

8.52 

6.96 

8.49 

7.00 

8.46 

7.03 

11 

12 

j 9.33 

7.55 

9.29 

7.59 

9.26 

7.63 

9.23 

7.67 

12 

13 

110.10 

8.18 

10.07 

8.23 

10.03 

8.27 

9.99 

8.31 

13 

14 

10.88 

i 8.81 

10.84 

8.86 

10.80 

8 . 91 

10.76 

8.95 

14 

15 

11.66 

9.44 

11.62 

9.49 

11.57 

9.54 

11.53 

9.59 

15 

16 

12.43 

10.07 

12.39 

10.12 

12.35 

10.18 

12.30 

10.23 

16 

17 

13.21 

10.70 

13.16 

10.76 

13.12 

10.81 

13.07 

10.87 

17 

18 

13.99 

11.33 

13.94 

11.39 

13.89 

11.45 

13.84 

11.51 

18 

19 

14.77 

11.96 

14.71 

12.02 

14.06 

12.09 

14.61 

12.15 

19 

20 

15.54 

12.59 

15.49 

12.65 

15.43 

12.72 

15.38 

12.79 

20 

21 

16.32 

13.22 

16.26 

13.29 

! 16.20 

13.36 

16.15 

13.43 

21 

22 

17. 10 

13.84 

17.04 

13.92 

1 16.98 

13.99 

16.91 

14.07 

22 

23 

17.87 

14.47 

17.81 

14.55 

17.75 

14.63 

17.68 

14.71 

23 

24 

13.65 

15.10 

18.59 

15.18 

18.52 

15.27 

18.45 

15.35 

24 

25 

19.43 

15.73 

19.36 

15.82 

19.29 

15.90 

19.22 

15.99 

25 

26 

20.21 

16.36 

20.13 

10.45 

20.00 

16.54 

19.99 

16.63 

26 

27 

20.98 

16.99 

20.91 

17.08 

20.83 

17.17 

20.76 

17.26 

27 

23 

21.76 

17.62 

21.68 

17.72 

21.61 

17.81 

21.53 

17.90 

28 

29 

22.54 

18.25 

22.46 

18.35 

22.38 

18.45 

22.30 

18.54 

29 

30 

23.31 

18.88 

23.23 

18.98 

23.15 

19.08 

23.07 

19.18 

30 

31 

24.09 

19.51 

24.01 

19.61 

23.92 

19.72 

23.83 

19.82 

31 

32 

24.87 

20.14 

24.78 

20.25 

24.69 

20.35 

24.60 

20.40 

32 

33 

25.65 

20.77 

25.55 

20.88 

25.46 

20.99 

25.37 

21.10 

33 

34 

26.42 

21.40 

26.33 

21.51 

26.24 

21.63 

26.14 

21.74 

34 

35 

27.20 

22.03 

27.10 

22.14 

27.01 

22.26 

26.91 

22.38 

35 

36 

27.98 

22.66 

27.88 

22.78 

27.78 

22.90 

27.63 

23.02 

3*6 

37 

28.75 

23.23 

28.65 

23.41 

28.55 

23.53 

28.45 

23.66 

37 

38 

29.53 

23.91 

29.43 

24.04 

29.32 

24.17 

29.22 

24.30 

33 

39 

30.31 

24.54 

30.20 

24.68 

30.09 

24.81 

29.98 

24.94 

39 

40 

31.09 

25.17 

30.98 

25.31 

30.86 

25.44 

30.75 

25.58 

40 

41 

31.86 

25.80 

31.75 

25.94 

31.04 

26.08 

31.52 

26.22 

41 

42 

32.64 

26.43 

32.52 

26.57 

32.41 

26.72 

32.29 

26.86 

42 

43 

33.42 

27.06 

33.30 

27.21 

33.18 

27.35 

33.06 

27.50 

43 

44 

34.19 

27.69 

34.07 

27.84 

33.95 

27.99 

33.83 

28.14 

44 

45 

34.97 

28.32 

34.85 

28.47 

34.72 

28.62 

34.60 

28.77 

45 

46 

35.75 

28.95 

35.62 

29.10 

35.49 

29.26 

35.37 

29.41 

46 

47 

36.53 

29.58 

36.40 

29.74 

36.27 

29.90 

36.14 

30.05 

47 

48 

37.30 

30.21 

37.17 

30.37 

37.04 

30.53 

36.90 

30.69 

48 

49 

38.08 

30.84 

37.95 

31.00 

37.81 

31.17 

37.67 

31.33 

49 

50 

38.86 

31.47 

38.72 

31.64 

38.58 

31.80 

38.44 

31.97 

50 

o' 

o 

c 

Dep. 

L^t. 

Dep. 

Lat. 

Dep. 

Lett* 

Dep. 

Lat. 

o' 

c 

c 

ri 

*-> 

W 

Q 

51 Deg. 

50f Deg. 

50} Deg. 

50} Deg. 

*-> 

VI 

Q 




























































































traverse table. 


81 


o 
►- • 

CO 

<“► 

p 

39 Deg. 

39} Deg. 

39£ Deg. 

39} Deg. 

C? 

►— • 

Uj 

p 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

n 

a 

51 

39.63 

32.10 

39.49 

32.27 

39.35 

32.44 

39.21 

32.61 

51 

52 

40.41 

32.72 

40.27 

32.90 

40.12 

33.08 

39.98 

33.25 

52 

53 

41.19 

33.35 

41.04 

33.53 

40.90 

33.71 

40.75 

33.89 

53 

54 

41.97 

33.98 

41.82 

34.17 

41.67 

34.35 

41.52 

34.53 

54 

55 

142.74 

31 61 

| 42.59 

34.80 

42.44 

34.98 

42.29 

35.17 

55 

56 

I 43.52 

i 35.24 

43.37 

35.43 

43.21 

35.62 

43.06 

35.81 

56 

57 

44.30 

35.87 

44.14 

36.06 

43.98 

36.26 

43.82 

36.45 

57 

58 

145.07 

36.50 

44.91 

36.70 

44.75 

36.89 

44.59 

37.09 

58 

59 

J 45.85 

37.13 

45.69 

37.33 

45.53 

37.53 

45.36 

37.73 

59 

60 

!46.63 

37.76 

46.46 

37.96 

46.30 

38.16 

46.13 

38.37 

60 

61 

.47.41 

38.39 

47.24 

38.60 

47.07 

38.80 

46.90 

39.01 

61 

62 

48.18 

39.02 

48.01 

39.23 

47.84 

39.44 

47.67 

39.65 

62 

63 

48.96 

39.65 

48.79 

39.86 

48.61 

40.07 

48.44 

40.28 

63 

64 

49.74 

40.28 

49.56 

40.49 

49.38 

40.71 

49.21 

40.92 

64 

65 

50.51 

40.91 

50.34 

41.13 

50.16 

41.35 

49.97 

41.56 

65 

66 

51.29 

41.54 

51.11 

41.76 

50.93 

41.98 

50.74 

42.20 

66 

67 

52.07 

42.16 

51.88 

42.39 

51.70 

42.62 

51.51 

42.84 

67 

68 

52.85 

42.79 

52.66 

43.02 

52.47 

43.25 

52.28 

43.48 

68 

69 

53.52 

43.42 

53.43 

43.66 

53.24 

43.89 

53.05 

44.12 

69 

70 

54.40 

44.05 

54.21 

44.29 

54.01 

44.53 

53.82 

44.76 

70 

71 

55.18 

44.68 

54.98 

44.92 

54.79 

45.16 

54.59 

45.40 

71 

72 

55.95 

45.31 

55.76 

45.55 

55.56 

45. SO 

55.36 

46.04 

72 

73 

56.73 

45.94 

56.53 

46.19 

56.33 

46.43 

56.13 

46.68 

73 

74 

57.51 

46.57 

57.31 

46.82 

57.10 

47.07 

56.89 

47.32 

74 

75 

58.29 

47.20 

58. OS 

47.45 

57.87 

47.71 

57.66 

47.96 

75 

76 

59.06 

47.83 

58.85 

48.09 

58.64 

48.34 

158.43 

48.60 

76 

77 

59.84 

48.46 

59.63 

48.72 

59.42 

48.98 

l59.20 

49.24 

77 

78 

60.62 

49.09 

60.40 

49.35 

60.19 

49.61 

j 59.97 

49.88 

78 

79 

61.39 

49.72 

61.18 

49.98 

60.96 

50.25 

60.74 

50.52 

79 

80 

62.17 

50.35 

61.95 

50.62 

61.73 

50.89 

j61.51 

51.16 

80 

81 

62.95 

50.97 

62.73 

51.25 

62.50 

51.52 

62.28 

51.79 

81 

82 

63.73 

51.60 

63.50 

51.88 

63.27 

52.16 

63.04 

52.43 

82 

83 

64.50 

52.23 

64.27 

52.51 

64.04 

52.79 

63.81 

53.07 

83 

84 

65.28 

52.86 

65.05 

53.15 

64.82 

53.43 

64.58 

53.71 

84 

85 

66.06 

53.49 

65.82 

53.78 

65.59 

54.07 

65.35 

54.35 

85 

86 

66.83 

54.12 

66.60 

54.41 

66.36 

54.70 

66.12 

54.99 

86 

87 

67.61 

54.75 

67.37 

55.05 

67.13 

55.34 

60.89 

55.63 

87 

88 

68.39 

55.38 

68.15 

55.68 

67.90 

55.97 

'67.66 

56.27 

88 

89 

69.17 

56.01 

68.92 

56.32 

68.67 

56.61 

68.43 

56.91 

89 

90 

69.94 

56.64 

69.70 

56.94 

69.45 

57.25 

69.20 

57.55 

90 

91 

70.72 

57.27 

70.47 

57.58 

70.22 

57.88 

69.96 

58.19 

91 

92 

71.50 

57.90 ; 

71.24 

58.21 

70.99 

58.52 

70.73 

58.83 

92 

93 

72.27 

58.53 i 

72.02 

58.84 1 

71.76 

59.16 

71.50 

59.47 

93 

94 

73.05 

59.16 ! 

72.79 

59.47 i 

72.53 

59.79 

72.27 

60.11 

94 

95 

73.83 

59.79 j 

73.57 

60.11 I 

73.30 

60.43 

73.04 

60.75 

95 

96 ! 74.61 

60.41 

74.34 

60.74 

74.08 

61.06 

73.81 

61.39 

90 

97 

75.38 

61.04 

75.12 

61.37 

74.85 

61.70 

74.58 

62.03 

97 

98 

76.16 

61.67 

75.89 

62.01 

75.62 

62.34 

75.35 

62.66 

98 

99 

76.94 

62.30 

76.66 

62.64 

76.39 

62.97 

76.12 

63.30 

99 

100 1 

77.71 

62.93 

77.44 

63.27 

77.16 

63.61 

76.88 

63.94 

100 

V 

« 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

v 

rj 

5 

>-» 

0Q 

a 

d 

.2 ! 
Q 1 

51 Deg. 

9 

50f Deg. 

50^ Deg. 

50} Deg*. 




















































































































C2 


TRAVERSE TAELE 


Distance. 

40 Deg. 

40$ Deg, 

40 £ Deg. 

o 

Deg. 

C 

c-* 

P ! 

Lat. ! 

i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep.. 

o 

p 

1 

0.77 

0.61 

0.76 

0.65 

0.76 

0.65 

0.7G 

0.65 

1 

2 

1.53 

1.29 

1.53 

1.29 

1.52 

1.30 

1.52 

1.31 

2 

3 

2.30 

1.93 

2.29 

1.94 

2.28 

1.95 

2.27 

1.96 

3 

4 

3.06 

2.57 

3.05 

2.58 

3.04 

2.60 ! 

3.03 

2.61 

4 

ft 

3.83 

3.21 

3.82 

3.23 

3.80 

3.25 i 

3.79 

3.26 

5 

C 

4.60 

3.86 

4.58 

3.88 

4.56 

3.90 ; 

4.55 

3.92 ! 

6 

7 

ft. 36 

4.50 

5.34 

4.52 

5.32 

4.55 | 

5.30 

4. 57 

7 

8 

6.13 

5.14 

6.11 

5.17 

6.08 

5.20 

6.06 

5.22 

8 

9 

6.89 

5.79 

6.87 

5.82 

6.84 

5.84 

6.82 

5. 87 

9 

10 

7.66 

6.43 

7.63 

6.46 

7.60 

6.49 

7.58 

6.53 

10 

i 1 

8.43 

7.07 

8.40 

7.11 

8.36 

7.14 

8.33 

7.18* 

11 | 

12 

9.19 

7.71 

9.16 

7.75 

9.12 

7.79 

9.09 

7.83 

12 

13 

9.96 

8.36 

9.92 

8.40 

9.89 

8.44 

9.85 

8.49 

13 

14 

10.72 

9.00 

10.69 

9.05 

10.65 

9.09 

10.61 

9.14 

14 

1ft 

11.49 

9.64 

11.45 

9.69 

11.41 

9.74 1 

11.36 

9.79 

15 

1G 

12.26 

10.28 

12.21 

10.34 

12.17 

10.39 

12.12 

10.44 

16 

17 

13.02 

10.93 

12.97 

10.98 

12.93 

11.04 

12.88 

11.10 

17 

IS 

13.79 

11.57 

13.74 

11.63 

13.69 

11.69 

13.64 

11.75 

18 | 

19 

14.55 

12.21 

14.50 

12.28 

14.45 

12.34 

14.39 

12.40 

19 

20 

15.32 

12.86 

15.26 

12.92 

15.21 

12.99 

15.15 

13.06 

20 

1 21 

16.09 

13.50 

16.03 

13.57 

15.97 

13.64 

15.91 

13.71 

21 

22 

16.85 

14.14 

16.79 

14.21 

16.73 

14.29 

16.67 

14.36 

22 

23 

17.62 

14.78 

17.55 

14.86 

17.49 

14.94 | 

17.42 ' 

15.01 

23 

24 

18.39 

15.48 

18.32 

15.51 

18.25 

15.59 

18.IS 

15.67 

24 

25 

19.15 

16.07 

19.08 

16.15 

19.01 

16.24 i 

18.94 

16.32 

25 

20 

19.92 

16.71 

19.84 

16.80 

19.77 

16.89 

19.70 

16.97 

26 

27 

20.68 

17.36 

20.61 

17.45 

20.53 

17.54 ; 

20.45 

17.62 

27 

28 

21.45 

18.00 

21.37 

18.09 

21.29 

IS.15 

21.21 

18.23 

28 

29 

22.22 

IS. 64 

22.13 

18.74 

22.05 

18.83 

21.97 

18.93 

29 

30 

22.98 

19.28 

22.90 

19.38 

22.81 

19.48 

22.73 

19.58 

30 

31 

23.75 

19.93 

23.68 

20.03 

23.57 

20.13 

!23.48 

20.24 

31 

32 

24.51 

20.57 

24.42 

20.68 

24.33 

20.78 

24.24 

20.89 

32 

33 

25.28 

21.21 

25.19 

21.32 

25.09 

21.43 

! 25.00 

21.54 

33 

34 

26.05 

21.85 

25.95 

21.97 

25.85 

22.08 

1 25.76 

22.19 

34 

35 

26.81 

22.50 

26.71 

22.61 

26.61 

22.73 

|26.51 

22.85 

35 

30 

27.58 

23.14 

27.48 

23.26 

27.37 

23.38 

j 27.27 

23.50 

36 

37 

28.34 

23.78 

28.24 

23.91 

28.13 

24.03 

128.03 

24*. 15 

37 

38 

29.11 

24.43 

29.00 

24.55 

28.90 

24.68 

i 28.79 

24.80 

| 38 

39 

29.88 

25.07 

29.77 

25.20 

29.66 

25.33 

29.54 

25.46 

39 

40 

30.64 

25.71 

30.53 

25.84 

30.42 

25.98 

30.30 

26.11 

40 

41 

31.41 

26.35 

31.29 

26.49 

31.18 

26.63 

31.06 

26.76 

41 

42 

32.17 

27.00 

32.06 

27.14 

31.94 

27.28 

31.82 

27.42 

42 

43 

132.94 

27.64 

32.82 

27.78 

32.70 

27.93 

32.58 

28.07 

I 43 

44 

33.71 

28.28 

33.58 

28.43 

33.46 

28.58 

I 33.33 

1 28.72 

| 44 

45 

34.47 

28.93 

34.35 

29.08 

34.22 

29.23 

1 34.09 

29.37 

45 

46 

35.24 

29.57 

35.11 

29.72 

34.98 

29.87 

34.85 

I 30.03 

46 

47 

36.00 

30.21 

35.87 

30.37 

35.74 

30.52 

35.61 

30.68 

47 

43 

36.77 

30.85 

36.64 

31.01 

36.50 

31.17 

36.36 

31.33 

48 

49 

37.54 

31.50 

37.40 

31.66 

37.26 

31.82 

37.12 

31.99 

49 

50 

1 38.30 

32.14 

38.16 

32.31 

38.02 

32.47 

37.88 

32.64 

50 

o' 

o 

c 

Dep. 

i Lat. 

Dep. 

j Lat. 

Dep. 

Lat. 

Dep. 

1 L ti t * 

1 

«j 

o 

c 

*-> 

.t/5 

s 

- 

P 

60 Deg. 

49| Deg. 

49£ Deg. 

49$ Deg. 

CJ 

.2 

1 C. 

j 






















































































































mAVERSE TABLE 


83 


o 

r'*' 

P 

40 Deg. 

40} Deg. 

40} Deg. 

40} Deg. 

Distance. 

3 

© 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

39.07 

32.78 

38.92 

32.95 

38.78 

33.12 

38.64 

33.29 

51 

52 

39.83 

33.42 

39.69 

33.60 

39.54 

33.77 

39.39 

33.94 

52 

53 

40.60 

34.07 

40.45 

34..24 

40.30 

34.42 

40.15 

34.60 

i 53 

54 

41.37 

34.71 

41.21 

34.89 

41.06 

35.07 

40.91 

35.25 l 54 

55 

42. 13 

35 . 35 

41.98 

35.54 

41.82 

35.72 

41.67 

35.90 

55 

56 

42.90 

36.00 

42.74 

36.18 

42.58 

36.37 

42.42 

36.55 

56 

57 

43.66 

36.64 

43.50 

36.83 

43.34 

37.02 

43.18 

'37.21 

57 

53 

41.43 

37.23 

44.27 

37.48 

44.10 

37.67 

43.94 

37.86 

58 

59 

45.20 

37.92 

45.03 

38.12 

44.86 

38.32 

44.70 

38.51 

59 

GO 

45.96 

33.57 

45.79 

38.77 

45.62 

38.97 

45.45 

39.17 

GO 

61 

46.73 

39.21 

46.5 6 

39.41 

46.38 

39.62 

46.21 

39.82 

61 

62 

'47.49 

39.85 

47.32 

40.06 

47.15 

40.27 

46.97 

40.47 

62 

63 

48.26 

40.50 

48.08 

40.71 

47.91 

40.92 

47.73 

41.12 

63 

64- 

49.03 

41.14 

43.85 

41.35 

j 48.67 

41.56 

48.48 

41.78 

64 

65 

49.79 

41.78 

49.01 

42.00 

! 49.43 

42.21 

49.24 

42.43 

65 

66 

50.56 

42.421 

50.37 

42.64 

50.19 

42.86 

50.00 

43.08 

66 

67 

51 .32 

43.07 i 

51.14 

43.29 

50.95 

43.51 

50.76 

43.73 

67 

63 

52.09 

43.71 

51.90 

43.94 

I 51.71 

44.16 

51.51- 

44.39 

68 

69 

52.86 

44.35 

52.66 

44.53 

j 52.47 

44.81 

52.27 

45.04 

69 

70 

53.62 

45.00 

53.43 

45.23 

53.23 

45.46 : 

53-03 

45.69 

70 

71 

54.39 

45.64 

54.19 

45.87 

53.99 

46.11 

53. 7 0 

46.35 

71 

72 

55.16 

46.28 

54.95 

46.52 

54.75 

46.76 1 

54.54 

47.00 

72 

73 

55.92 

46.92 

55.72 

47.17 j 

1 55.51 

47.41 

55.30 

47.65 

73 

74 

56.69 

47.57 

56.48 

47.81 

56.27 

43.08 

56.06 

48.30 

74 

75 

57.45 

48.21 

57.24 

48.46 

57.03 

48.71 

56.82 

43.96 

75 

76 

58.22 

48.85 

53.01 

49.11 

57.79 

49.36 

57.57 

49.61 

76 

77 

58.99 

49.49 

53 . 77 

49.75 

58.55 

50.01 

58.33 

50.26 

77 

73 

59.75 

50. ] 4 

59,53 

50.40 

59.31 

50.66 

59.09 

50.92 

78 

79 

60.52 

50.78 

60.30 

51.04 

60.07 

51.31 

59.85 

51.57 

79 

80 

61.23 

51.42 

61.06 

51.69 

60.83 

51.96 

60.61 

52.22 

80 

81 

62.05 

52.07 

61.82 

52.34 | 

61.59 

52.61 

61.36 

52.87 

81 

83 

62.82 

52.71 

62.59 

52.98 i 

62.35 

53 . 25 

62.12 

53.53 

82 

83 

63.58 

53.35 

63.35 

53 . 63 1 

63.11 

53.90 

62.88 

54.18 

83 

84 

64.35 

53.99 

64.11 

54.27 

63.87 

54.55 

63.64 

54.83 

84 

85 

65. 11 

54.04 

64.87 

54.92 

61-63 

55 . 20 

64.39 

55.48 

85 

86 

65.88 

55.28 

65.64 

55 . 57 

65-39 

55.85 

65.15 

56.14 

86 

87 

66.65 

55.92 

66.40 

56.21 

66.16 

56.50 

65.91 

56.79 

87 

88 

67.41 

56.57 

67.16 

56.8 6 

68.92 

57.15 

66.67 

57.44 

88 

89 

63.18 

57.21 

67.93 

57.50 

67.68 

57.SO 1 

67.42 

58.10 

89 

90 

68.94 

57.85 

63.69 

58.15 

68.44 

53.45 

68.18 

58.75 

90 

91 

69.71 

58.49 

69.45 

58.80 j 

69.20 

59.10 

68.94 

59.40 

91 

92 

70.48 

59.14 

70.22 

59.44 j 

69.96 

59.75 

69.70 

60.05 

92 

93 

71.24 

59.78 

70.93 

60.09 

70.72 

60.40 

70.45 

60.71 

93 

94 

72.01 

60.42 

71.74 

60 . 74 

71.48 

61.05 

71.21 

61.36 

94 

95 

72.77 

61.06 

72.51 

61.38 

72.24 

61.70 

71.97 

62.01 

95 

95 

73 . 54 

61.71 

73.27 

62.03 

73.00 

62.35 

72 . 73 

62 . 66 

96 

97 

74 . 31 

62.35 

74.03 

62.67 

73 . 76 

63.00 

73.48 

63.32 

97 

98 

75.07 

62.99 

74.80 

63.32 

74.52 

63.65 

74.24 

63.97 

98 

99 

75 . 84 

63.64 

75.56 

63.97 

75.28 

64.30 

75 . 00 

64.62 

99 

100 

76.60 

64.28 

76.32 

64.61 

76.04 

64.94 

75.7 C 

65.23 

100 

6 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

d 

o 

c 

rf ; 

M ! 

Q 

50 Dog. 

49} Deg. 

49} Deg. 

49} Deg. 

■4-i 

'Ji 

/£ 


















































































































84 


TRAVERSE TABLE 


Distance. 

41 Deg. 

41^ Deg. 

4H 

Deg. 

41| Deg. 

Dista 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

O 

o 

1 

0.75 

0.66 

0.75 

0.C6 

0.75 

0.66 

0.75 

0.67 

1 

O 

/W 

1.51 

1.31 

1.50 

1.32 

1.50 

1.33 

1.49 

1.33 

2 

3 

2.26 

1.97 

2.26 

1.98 

2.25 

1.99 

2.24 

2.00 

3 

4 

3.02 

2.62 

3.01 

2.64 

3.00 

2.65 

2.98 

2.66 

4 

5 

3.77 

3.28 

3.78 

3.30 

3.74 

3.31 

3.73 

3.33 

5 

6 

4.53 

3.94 

4.51 

3.96 

4.49 

3.98 

4.48 

4.00 

6 

7 

5.28 

4.59 

5.26 

4.62 

5.24 

4.64 

5.22 

4.66 

7 

8 

6.04 

5.25 

6.01 

5.27 

5 99 

5.30 

5.97 

5.33 

8 

9 

6.79 

5.90 

6.77 

5.93 

6.74 

5.96 

6.71 

5.99 

9 

10 

7.55 

6.56 

7.52 

6.59 

7.49 

6.63 

7.46 

6.66 

10 

11 

8.30 

7.22 

8.27 

7.25 

8.24 

7.29 

8.21 

7.32 

11 

12 

9.06 

7.87 

9.02 

7.91 

8.99 

7.95 

8.95 

7.99 

12 

13 

9.81 

8.53 

9.77 

8.57 

9.74 

8.61 

9.70 

8.66 

13 

14 

10.57 

9.18 

10.53 

9.23 

10.49 

9.28 

10.44 

9.32, 

14 

15 

11.32 

9.84 

11.28 

9.89 

11.23 

9.94 

11.19 

9.99 

15 

15 

12.08 

10.50 

12.03 

10.55 

11.98 

10.60 

11.94 

10.65 

16 

17 

12.83 

11.15 

12.78 

11.21 

12.73 

11.26 

12.68 

11.32 

17 

18 

13.58 

11.81 

13.53 

11.87 

13.48 

11.93 

13.43 

11.99 

1.8 

19 

14.34 

12.47 

14.28 

12.53 

14.23 

12.59 

14.18 

12.65 

19 

20 

15.09 

13.12 

15.04 

13.19 

14.98 

13.25 

14.92 

13.32 

20 

21 

15.85 

13.78 

15.79 

13.85 

15.73 

13.91 

15.67 

13.98 

21 

22 

16.60 

14.43 

16.54 

14.51 

16.48 

14.58 

16.41 

14.65 

22 

23 

17.36 

15.09 

17.29 

15.16 

17.23 

15.24 

17.16 

15.32 

23 

24 

18.11 

15.75 

18.04 

15.82 

17.97 

15.90 

17.91 

15.98 

24 

25 

18.87 

16.40 

18.80 

16.48 

18.72 

16.57 

18.65 

16.65 

25 

26 

19.62 

17.06 

19.55 

17.14 

19.47 

17.23 

19.40 

17.31 

26 

27 

20.33 

17.71 

20.30 

17.80 

20.22 

17.89 

20.14 

17.98 

27 

28 

21.13 

18.3'? 

21.05 

18.46 

20.97 

18.55 

20.89 

18.64 

23 

29 

21.89 

19.03 

21.80 

19.12 

21.72 

19.22 

21.64 

19.31 

29 

30 

22.64 

19.08 

22.56 

19.78 

22.47 

19.88 

22.38 

19.98 

30 

31 

23.40 

20.34 

23.31 

20.44 

23.22 

20.54 

23.13 

20.64 

31 

32 

24.15 

20.99 

24.06 

21.10 

23.97 

21.20 

23.87 

21.31 

32 

33 

24.91 

21.65 

24.81 

21.70 

24.72 

21.87 

24.62 

21.97 

33 

34 

25.66 

22.31 

25.56 

22.42 

25.46 

22.53 

25.37 

22.64 

34 

35 

26.41 

22.96 

26.31 

23.08 

26.21 

23.19 

26.11 

23.31 

35 

36 

27.17 

23.62 

27.07 

23.74 

26.96 

23.85 

26.86 

23.97 

36 

37 

27.92 

24.27 

27.82 

24.40 

27.71 

24.52 

27.60 

24.64 

37 

38 

28.68 

24.93 

28.57 

25.00 

28.45 

25.18 

28.35 

25.30 

38 

39 

29.43 

25.59 

29.32 

25.71 

29.21 

25.84 

29.10 

25.97 

39 

40 

30.19 

26.24 

30.07 

26.37 

29.96 

26.50 

29.84 

26.64 

40 

41 

30.94 

26.90 

30.83 

27.03 

30.71 

27.17 

30.59 

27.30 

41 

42 

31.70 

27.55 

31.58 

27.69 

31.46 

27.83 

31.33 

27.97 

42 

43 

32.45 

28.21 

132.33 

28.35 

32.21 

28.49 

32.08 

28.63 

43 

44 

33.21 

28.87 

33.08 

29.01 

32.95 

29.16 

32.83 

29.30 

44 

45 

33.96 

29.52 

33.83 

29.67 

33.70 

29.82 

33.57 

29.97 

45 

46 

34.72 

30.18 

34.58 

30.33 

34.45 

30.48 

34.32 

30.63 

46 

47 

35.47 

30.83 

35.34 

30.99 

35.20 

31.14 

35.06 

31.30 

47 

48 

36.23 

31.49 

36.09 

31.65 

35.95 

31.81 1 

35.81 

31.96 

43 

49 

30.98 

32.15 

36.84 

32.31 

36.70 

32.47 

36.56 

32.63 

49 

50 

37.74 

32.80 

37.59 

32.97 

37.45 

33.13 

37.30 

33.29 

50 

d 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 Lat. 

d 

o 

C 

d 

w 

5 

49 Deg. 

48f Deg. 

48^ Deg. 

48$ Deg. 

rt 

Cti 

• —» 

ft 


































































































instance, cotocootcootoi-' nnnnnnnnnoo cocooooooooooooooco ao5<J>o»o>a(»oo •ooirc'isi< 


TRAVERSE TABLE. 


85 


41 Deg. 

41 i Deg. 

41$ Deg. 

41J Deg. : 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Cep. 

33.49 

33.46 

38.34 

33.63 

38.20 

33.79 

38.05 

33.96 

51 

39.24 

34.12 

39.10 

34.29 

38.95 

34.46 

33.79 

34.63 

52 

40.09 

34.77 

39.85 

34.95 

39.69 

35.12 

39.54 

35.29 

53 

40.75 

35.43 

40.60 

35.60 

40.44 

35.78 

40.29 

35.96 

54 

41.51 

36.08 

41.35 

36.26 

41.19 

36.44 

41.03 

36.62 

55 

42.26 

36.74 

42.10 

36.92 

41.94 

37.11 

41.78 

37.29 

56 

43.02 

37.40 

42.85 

37.58 

42.69 

37.77 

42.53 

37.96 

57 

43.77 

33.05 

43.61 

38.24 

43.44 

38.43 

43.27 

38.62 

5S 

44.53 

38.71 

44.36 

38.90 

44.19 

39.09 

44.02 

39.29 

59 

45.28 

39.36 

45.11 

39.56 

44.94 

39.76 

44.76 

39.95 

60 

46.04 

40.02 

45.86 

40.22 

45.69 

40.42 

45.51 

40.62 

61 

46.79 

40.68 

46.61 

40.88 

46.44 

41.08 

46.26 

41.28 

62 

47.55 

41.33 

47.37 

41.54 

47. IS 

41.75 

47.00 

41.95 

63 

48.30 

41.99 

48.12 

42.20 

47.93 

42.41 

47.75 

42.62 

64 

49.06 

42.64 

48.87 

42.86 

48.6S 

43.07 

48.49 

43.28 

65 

149.81 

43.30 

49.62 

43.52 

49.43 

43.73 

49.24 

43.95 

66 

50.57 

43.96 ; 

50.37 

44.18 

50.18 

44.40 

49.99 

44.61 

67 

51.32 

44.61 

51.13 

44.84 

50.93 

45.06 

50.73 

45.28 

68 

52.07 

45.27 

51.88 

45.49 

51.68 

45.72 

51.43 

45.95 

69 

52.83 

45.92 

52.63 

46.15 

52.43 

46.38 

52.22 

46.61 

70 

53.58 

46.58 

53.38 

46.81 

53.18 

47.05 

52.97 

47.28 

71 

54.34 

47.24 

54.13 

47.47 

53.92 

47.71 

53.72 

47.94 

72 

55.09 

47.89 

54.88 

43.13 

54.67 

48.37 

54.46 

48.61 

73 

55.85 

48.55 

55.64 

48.79 

55.42 

49.03 

55.21 

49.28 

74 

56.60 

49.20 

56.39 

49.45 

56.17 

49.70 

55.95 

49.94 

75 

57.36 

49.86 

57.14 

50.11 

56.92 

50.36 

56.70 

50.61 

76 

58. 11 

50.52 

57.89 

50.77 

57.67 

51.02 

57.45 

51.27 

77 

58.87 

51.17 

58.64 

51.43 

58.42 

51.6S 

58.19 

51.94 

78 

59.62 

51.83 

59.40 

52.09 

59.17 

52.35 

!58.94 

52.60 

79 

60.38 

52.48 

60.15 

52.75 

59.92 

53.01 

59.68 

53.27 

80 

61.13 

53.14 

60.90 

53.41 

60.67 

53.67 

60.43 

53.94 

81 

61.89 

53.80 

61.65 

54.07 

61.41 

54.33 

61.18 

54.60 

82 

62.64 

54.45 

62.40 

54.73 

62.16 

55.00 

61.92 

55.27 

83 

63.40 

55.11 

63.15 

55.33 

62.91 

55.66 

62.67 

55.93 

84 

64.15 

55.76 

63.91 

56.04 

63.66 

56.32 

63.41 

55.60 

85 

64.90 

56.42 

64.66 

56.70 

64.41 

56.99 

64.16 

57.27 

88 

65.66 

57.08 

65.41 

57.36 

65.16 

57.65 

64.91 

57.93 

87 

66.41 

57.73 

66.16 

58.02 

65.91 

58.31 

165.65 

58.60 

88 

67.17 

58.39 

66.91 

58.68 

66.66 

58.97 

66.40 

50.26 

89 

67.92 

59.05 

67.67 

59.34 

67.41 

59.64 

67.15 

59.93 

90 

68.68 

59.70 

63.42 

60.00 

68.15 

60.30 

67.89 

60.60 

91 

69.43 

60.36 

69.17 

60.66 

68.90 

60.96 

68.64 

61.26 

92 

70.19 

61.01 

69.92 

61.32 

69.65 

61.62 

69.38 

61.93 

93 

70.94 

61.67 

70.67 

61.93 

70.40 

62.29 

70.13 

62.59 

94 

71.70 

62.33 

71.43 

62.64 

71.15 

62.95 

70.88 

63.26 

95 

72.45 

62.98 

72.18 

63.30 

71.90 

63.61 

71.62 

63.92 

96 

73.21 

63.64 

72.93 

63.96 

72.65 

64.27 

72.37 

64.59 

97 

73.96 

64.29 

73.68 

64.62 

73.40 

64.94 

73.11 

65.26 

98 

74.72 

64.95 

74.43 

65.28 

74.15 

65.60 

73.86 

65.92 

99 

75.47 

65.61 

75.18 

65.93 

74.90 

66.26 

74.81 

66.59 

100 

Dcp 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dnp. 

Lat. 

or 

o 

e 

49 Deg. 

48f Deg. 

48$ Deg. 

48$ Deg. 

i 

d 

*4 

0Q 

5 


















































































































86 


TBAVEKSK TABLE 


O 

XA 

r> 

42 Deg. 

42J Deg. 

42^- 

Deg. 

421 Deg. 

O 

7V 

P 

3 

O 

Q 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

CD 

1 

0.74 

0.67 

0.74 

0.67 

0.74 

0.68 

0.73 

0.68 

1 

o 

/V 

1.49 

1.34 

1.48 

1.34 

1.47 

1.35 

1.47 

1 .36 

o 

•q 

3 

2.23 

2.01 

2.22 

2.02 

2.21 

2.03 

2.20 

2.04 

3 

4 ! 

2.97 

2.68 

2.96 

2.69 

2.95 

2.70 

2.94 

2 . 72 

4 

6 

3.72 

o or. 

O • Ot) 

3.70 

3.36 

3.69 

3.38 

3.67 

3.39 

5 

0 

4.46 

4.01 

4.44 

4.03 

4.42 

4.05 

4.41 

4.07 

fi 

7 

5.20 

4.68 

5.18 

4.71 

5.16 

4.73 

5.14 

4.75 

7 

8 

5.95 

5.35 

5.92 

5.38 

5.90 

5.40 

5.87 

5.43 

8 

9 

6.69 

6.02 

6.66 

6.05 

6.64 

6.08 

6.01 

6.11 

o 

10 

7.43 

6.69 

7.40 

6.72 

7.37 

6.78 

7.34 

0.79 

10 

11 

8.17 

7.36 

8.14 

7.40 

8.11 

7.43 | 

8.08 

7.47 

11 

12 

8.92 

8.03 

8.88 

8.07 

8.85 

8.11 

8.81 

8.15 

12 

13 

9.66 

8.70 

9.62 

8.74 

9.58 

8.78 

9.55 

8.82 

13 

14 

10.40 

9.37 

10.36 

9.41 

10.32 

9.46 

10.28 

9.50 

14 

15 

11.15 

10.04 

11.10 

10.09 

11.06 

10.13 

11.01 

10. IS 

15 

16 

11.89 

10.71 

11.84 

10.76 

11.80 

10.81 

11.75 

10.86 

16 

17 

12.63 

11.38 

12.58 

1L .43 

12.53 

11.48 

12.48 

11.54 

17 

18 

13.38 

12.04 

13.32 

12.10 

13.27 

12.16 

13.22 

12.22 

18 

19 

14.12 

12.71 

14.06 

12.77 

14.01 

12.84 

13.95 

12.90 

19 

20 

14.86 

13.38 

14.80 

13.45 

14.75 

13.51 

14.69 

13.59 

20 

21 

15.61 

14.05 

15.54 

14.12 

15.48 

14.19 

15.42 

14.25 

21 

22 

16.35 

14.72 

16.28 

14.79 1 

16.22 

14.86 

16.16 

14.93 

22 

23 

17.09 

15.39 

17.02 

15.46 

16.96 

15.54 1 

16.89 

15.61 

23 

24 

17.84 

16.06 

17.77 

16.14 

17.69 

16.21 ! 

17.62 

16.29 

24 

25 

18.53 

16.73 

18.51 

16.81 

13.43 

16.S9 

18.36 

16.97 

25 

26 

19.32 

17.40 

19.25 

17.48 

19.17 

17.57 

19.09 

17.65 

26 

27 

20.06 

18.07 

19.99 

18.15 

19.91 

18.24 1 

19.83 

18.33 

27 

2S 

20.81 

18.74 

20.73 

18.83 

20.61 

18.92 ; 

20.56 

19.01 

28 

29 

21.55 

19.40 

21.47 

19.50 

21.39 

19.59 i 

21.80 

19.69 

29 

30 

22.29 

20.07 

22.21 

20.17 

22.12 

20.27 

22.03 

20.36 

30 

31 

23.04 

20.74 

22.95 

20.84 

22.86 

20.94 

22.76 

2 L. 04 

31 

32 

23.78 

21.41 

23.69 

21.52 

23.59 

21.62 

23.50 

21.72 

32 

33 

24.52 

22.03 

24.43 

22. 19 

24.33 

22.29 

24.23 

22.40 

33 

34 

25.27 

22.75 

25.17 

22.86 

25.07 

22.97 

24.07 

23.08 

34 

35 

26.01 

23.42 

25.91 

23.53 

25.80 

23.65 

25.70 

23.76 

35 

36 

26.75 

24.09 

26.65 

24.21 

26.54 

24.32 

26.44 

24.44 

36 

37 

27 50 

24.76 

27.39 

24.88 

27.28 

i 25.00 

27.17 

25. 12 

37 

33 

28.24 

25.43 

23.13 

25.55 

28.02 

25.07 

27.90 

25.79 

38 

39 

23.93 

26.10 

28.87 

26.22 

28.75 

26.35 

28.64 

26.47 

39 

40 

29.73 

26.77 

29.61 

26.89 

29.49 

27.02 

29.37 

27.15 

40 

41 

130.47 

27.43 

30 . 35 

27.57 

30.23 

27.70 

|30. i l 

27.83 

41 

42 

'31.21 

28.10 

31.09 

28.24 

30.97 

28.37 

30.84 

28.5 l 

42 

43 

1 31.96 

28.77 

31.83 

28.91 

31.70 

29.05 

1 31.58 

29.19 

43 

• 44 

1 32.70 

29.44 

32.57 

29.58 

32.44 

29.73 

!32.31 

29.87 

44 

45 

33.44 

30 . 11 

33.31 

30.26 

33.18 

30.40 

33.04 

30 . 55 

45 

4G 

34.18 

30.78 

34.05 

30.93 

33.91 

31.08 

133.78 

31 .22 

46 

47 

0.1 1,0 
Ot • •J 

31.45 

34.79 

31.60 

34.65 

31.75 

!34.51 

31.90 

47 

48 

35.67 

32.12 

35.53 

32.27 

35.39 

32.43 

35.25 

32.58 

48 

49 

36.41 

32.79 

36.27 

32.95 

36.13 

33.10 

35.93 

33.26 

49 

50 

37.16 

33.46 

37.01 

33.62 

38.86 

33.78 

36.72 

33.94 

50 

cl 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dcp. 

Lat. 

C 

rj 

c3 
♦.» 

C/3 

5 

43 Deg. 

47f Deg. 

474 Deg. 

47^ Deg. 

■. vocj-i. g'Jgva »■ i— . .tv— .iw 

ci 

75 k 

o ! 








































































































TRAVERSE TABLE 


87 


Distance, j 

i 

42 Deg. 

42} Deg. 

42} Deg 

• 

42f Deg. 

a 
►— • 
cc 
ri 

P 

D 

O 

ct> 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dop. 

Lat. 

De 

P- 

51 i 

37. 

90 

34. 

13 

37. 

75 

34. 

29 

37. 

60 

34. 

46 

37. 

45 

34. 

62 

51 

e;o 
•) * 

33 

64 

34. 

79 

33. 

49 

34. 

96 

33. 

34 

35. 

13 

33. 

18 

35. 

30 

52 

53 1 

39 

39 

35 

46 

39. 

23 

35. 

64 

39. 

08 

35. 

81 

38. 

92 

35. 

93 

53 

54 | 

40. 

13 j 

36 

13 

39. 

97 

36. 

31 

39. 

81 

36. 

48 

39. 

65 

36. 

66 

51 

55 ! 

40 

87 

36 

80 

40. 

71 

36. 

98 

40 

55 

37. 

16 

40. 

39 

37. 

33} 

55 

56 

41 

62 

37. 

47 

41. 

45 

37. 

65 

41. 

29 

37. 

S3 

41. 

12 

33. 

0 l| 

56 

57 

42 

36 

38 

14 

42. 

19 

38. 

32 

42. 

02 

38. 

51 

41. 

86 

38. 

69 1 

57 

58 

43 

10 

33 

81 

42. 

93 

39. 

00 

42. 

76 

39. 

IS 1 

42. 

59 

39. 

37 

58 

59 

43 

85 

39 

43 

43. 

67 

39. 

67 

43. 

50 

39. 

86 1 

43. 

32 

40. 

05 1 

59 

60 

44 

.59 

40 

15 

44 

41 

40. 

34 

44. 

24 

40. 

54 ! 

44. 

06 

40. 

73 | 

60 

61 

45 

.33 

40 

.32 

45 

15 

41 

01 

44. 

97 

41. 

2! i 

44. 

79 j 

41 

41 

61 

62 

46 

.07 

41 

.49 

45 

89 

41 

69 

45 

71 

41. 

89 j 

45. 

53 

42. 

09 

62 

63 

46 

.82 

42 

.16 

46 

63 

42 

36 

46 

45 

42 

56 

46. 

26 

42. 

76 

63 

64 

47 

56 

42 

.82 

47 

37 

43 

03 

47 

19 

43 

24 

47 

00 

43. 

44 

64 

65 

43 

.30 

43 

.49 

43 

1 l 

43 

70 

47 

92 

43 

91 

47. 

73 

44. 

12 

65 

66 

49 

05 

44 

. 16 

48 

.85 

44 

38 

48 

66 

44 

59 

48 

47 

44. 

80 

66 

67 

49 

.79 

44 

.83 

49 

.59 

45 

05 

49 

40 

45 

.26 

49 

20 

45 

48 

67 

68 

50 

.53 

45 

.50 

50 

.33 

45 

.72 

50 

.13 

45 

.94 

49 

93 

46 

16 

68 

69 

51 

.28 

46 

.17 

51 

.07 

46 

.39 

50 

.87 

46 

.62 

50 

67 

46 

84 

69 

70 

52 

.02 

46 

.84 

51 

.82 

47 

.07 

51 

.61 

47 

.29 

j 51 

40 

47 

o 2 

70 

71 

52 

.76 

47 

.51 

52 

.56 

47 

.74 

I 52 

.35 

47 

.97 

| 52 

14 

43 

19 

71 

72 

53 

.51 

48 

.18 

! 53 

.30 

48 

.41 

j 53 

.08 

48 

.64 

1 52 

.87 

43 

.87 

72 

73 

54 

.25 

43 

.85 

54 

.04 

49 

.08 

53 

.82 

49 

oh 

o -V 

153 

.01 

49 

55 

73 

74 

51 

.99 

49 

. 52 

54 

. 7S 

49 

.76 

54 

. 56 

49 

.99 

1 54 

.34 

50 

.23 

74 

75 

55 

.74 

50 

. 18 

55 

.52 

50 

.43 

55 

.30 

50 

.67 

55 

.07 

50 

.91 

75 

76 

56 

.48 

50 

.85 

56 

.26 

51 

.10 

56 

.03 

51 

.34 

55 

.SI 

51 

.59 

76 

77 

57 

oo 

51 

.52 

57 

.00 

51 

.77 

56 

.77 

52 

.02 

56 

.54 

52 

.27 

77 

78 

57 

.97 

52 

.19 

57 

.74 

52 

.44 

57 

. 51 

52 

.70 

.> / 

.28 

52 

.95 

73 

79 

58 

.71 

52 

.86 

53 

.43 

53 

.12 

58 

.24 

53 

.37 

5S 

.01 

53 

.03 

79 

80 

59 

.45 

53 

.53 

59 

.22 

53 

.79 

58 

.98 

54 

. 05 

53 

.75 

54 

.30 

80 

81 

60 

. 19 

54 

.20 

59 

.96 

51 

.46 

59 

.72 

54 

.72 

59 

.48 

54 

.98 

81 

82 

00 

.94 

54 

.87 

60 

.70 

55 

.13 

60 

.46 

55 

.40 

60 

.21 

55 

.68 

82 

83 

61 

.63 

55 

.54 

61 

.44 

55 

.81 

61 

.19 

56 

.07 

60 

.95 

56 

.34 

83 

84 

62 

.42 

56 

.21 

62 

.13 

56 

.48 

61 

.93 

56 

.75 

61 

.68 

57 

.02 

84 

85 

63 

.17 

58 

.88 

62 

.92 

57 

. 15 

62 

.67 

57 

.43 

62 

.42 

57 

.70 

85 

86 

63 

.91 

57 

.55 

63 

.66 

57 

.82 

1 63 

.41 

58 

. 10 

63 

. 15 

58 

.3:3 

86 

87 

64 

.65 

53 

.21 

64 

.40 

58 

.50 

J 64 

. 14 

58 

.78 

63 

.89 

59 

.06 

87 

88 

65 

.40 

53 

.88 

65 

. 14 

59 

.17 

64 

.83 

59 

.45 

64 

.62 

59 

.73 

83 

89 

66 

.14 

59 

. 55 

65 

.83 

59 

.84 

65 

.62 

60 

.13 

65 

.35 

60 

.41 

89 

99 

66 

.38 

60 

. 22 ' 

66 

.62 

60 

.51 

66 

.35 

60 

.80 

66 

.09 

61 

.09 

90 

91 

67 

.63 

60 

.89 

67 

.35 

61 

.19 

67 

.09 

61 

.48 

66 

.82 

61 

.77 

91 

92 

08 

.37 

61 

.56 

68 

.10 

61 

.86 

67 

.83 

62 

.15 

67 

.56 

62 

.45 

92 

93 

69 

.11 

62 

.23 

63 

.34 

62 

.53 

63 

.57 

62 

.83 

68 

.29 

63 

.13 

93 

94 

69 

.86 

62 

.90 

69 

.58 

63 

.20 

69 

.30 

63 

.51 

69 

.03 

63 

. 8 ) 

94 

95 

70 

.60 

63 

.57 

70 

.32 

63 

.87 

70 

.04 

64 

.18 

69 

. 76 

64 

.49 

95 

96 

71 

.34 

64 

.24 

71 

.08 

64 

.55 

70 

.78 

64 

.86 

I 70 

.49 

65 

.16 

96 

97 

72 

.03 

64 

.91 

71 

.80 

65 

.22 

71 

.52 

65 

.53 

71 

.23 

65 

.81 

97 

98 

72 

.83 

65 

.57 

72 

.54 

65 

.89 

72 

.25 

66 

.21 

71 

.96 

60 

.52 

93 

99 

73 

.57 

66 

.24 

73 

.28 

65 

.56 

72 

.99 

66 

.88 

72 

.70 

67 

.20 

99 

109 

74 

.31 

66 

.91 

74 

.02 

67 

.24 

73 

.73 

67 

. 56 

73 

.43 

67 

.88 

100 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

0 

£ 

d 

(4 

• 

Q 

43 Deg. 

471 Deg 


471 Deg. 

1 

47} Deg. 


















































































































88 


TRAVERSE TABLE. 


Distance. 

43 Deg. 

43i Deg 


43$ Deg 

• 

431 Deg. 

Distance.! 

I 

i 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0 

.73 

0 . 

68 

0.73 

0 . 

69 

0 

. 73 

0 . 

69 

0 

.72 

0 . 

69 

1 

2 

1 

.46 

1 . 

36 

1.46 

1 . 

37 

1 

.45 

1 . 

38 

1 

.44 

1 

33 

2 

3 

2 

.19 

2 . 

05 

2.19 

2 . 

06 

2 

.18 

2 . 

07 

2 

.17 

2 . 

07 

3 

4 

2 

.93 

2 . 

73 

2.91 

2 . 

74 

2 

.90 

O 
*y • 

75 

2 

.89 

O 

77 

4 

5 

3 

.66 

3. 

41 

3.64 

3. 

43 

3 

.63 

3. 

44 

3 

.61 

3. 

46 

5 

G 

4 

.39 

' 4. 

09 

4.37 

4. 

11 

4 

.35 

4. 

13 

4 

.33 

4. 

15 

6 

7 

5 

.12 

4. 

77 

5.10 

4. 

80 

5 

.03 

4. 

82 

5 

.06 

4. 

84 

7 

8 

5 

.85 

5. 

46 

5.83 

5. 

43 

5 

.80 

5. 

5.1 

5 

.78 

5. 

53 

8 

9 

6 

.58 

6 . 

14 

6.58 

6 . 

17 

6 

.53 

6 . 

20 

6 

.50 

6 . 

22 

9 

10 

7 

.31 

6 . 

82 

7.23 

6 . 

85 

7 

.25 

6 . 

88 

7 

.22 

6 

92 

10 

11 

8 

.04 

7. 

50 | 

8.01 

7. 

54 

7 

.98 

7. 

57 

7 

.95 

7. 

61 

11 

12 

8 

.78 

8 . 

18 

8.74 

8 . 

22 

8 

.70 

8 . 

26 

8 

.67 

8 . 

30 

12 

13 

9 

.51 

8 . 

87 ! 

9.47 

8 . 

91 

9 

.43 

8 . 

95 

9 

.39 

8 . 

99 

13 

14 

10 

.24 

9. 

55 i 

10.20 

9. 

59 

10 

.16 

9. 

64 

10 

.11 

9. 

68 

14 

15 

10 

.97 

10 . 

23 j 

10.93 

10 . 

28 

10 

.88 

10 . 

33 

10 

.84 

10 . 

37 

15 

16 

11 

.70 

10 . 

91 1 

11.65 

10 . 

96 

11 

.61 

11 . 

01 

11 

.56 

11 . 

06 

16 

17 

12 

.43 

11 . 

59 

12.33 

11 . 

65 

12 

.33 

11 . 

70 

12 

.28 

11 . 

76 

17 

18 

13 

. 16 

12 . 

28 ! 

13.11 

12 . 

33 

13 

.06 

'12. 

39 

13 

.00 

12 . 

45 

18 

19 

13 

.90 

12 . 

96 j 

13.84 

13. 

02 

13 

. 7S 

13. 

08 

13 

.72 

13. 

14 

19 

20 

14 

.63 

13. 

64 i 

14.57 

13. 

70 

14 

.51 

) 3. 

77 

14 

.45 

13. 

83 

20 

21 

15 

. 36 

14. 

32 

15.30 

14. 

39 

15 

.23 

14. 

46 

15 

.17 

14. 

52 

21 

22 

16 

.09 

15. 

09 

1 5 .02 

15. 

07 

15 

.96 

15. 

14 

15 

.89 

15. 

21 

22 

23 

16 

.82 

15. 

69 

16.75 

15. 

76 

16 

. 68 

15. 

83 

16 

.61 

15. 

90 

23 

24 

17 

.55 

16. 

37 

17.48 

16. 

44 

17 

.41 

16. 

52 

17 

.34 

16. 

60 

24 

25 

18 

.23 

17. 

05 

18.21 

17. 

13 

18 

.13 

17. 

21 

18 

.03 

17. 

29 

25 

26 

19 

.02 

17. 

73 

18.94 

17. 

81 

18 

.86 

17. 

90 

18 

.78 

1-7. 

98 

26 

27 

19 

.75 

18. 

41 

19.67 

13 

50 

19 

.59 

18. 

59 

19 

.50 

18. 

67 

27 

28 

20 

.48 

19. 

10 

20.39 

19. 

19 

20 

.31 

19. 

27 

20 

.23 

19. 

36 

28 

29 

21 

.21 

19. 

78 

21.12 

19. 

87 

21 

.04 

19. 

96 

20 

.95 

20 . 

05 

29 

30 

21 

.94 

20 . 

46 

21.85 

20 . 

56 

21 

.76 

20 . 

65 

21 

.67 

20 . 

75 

30 

31 

22 

.67 

21 . 

14 

22.58 

21 . 

24 

22 

.49 

21 . 

34 

22 

.39 

21 . 

44 

31 

32 

23 

.40 

21 . 

82 

23.31 

21 . 

93 

23 

.21 

22 . 

03 

23 

.12 

OO 

Aw Ay 

13 

32 

33 

24 

.13 

22 . 

51 

24.04 

22 . 

61 

23 

.94 

22 . 

72 

23 

.84 

*>c> 

Ay Ay 

82 

33 

34 

24 

.87 

23. 

19 

24.76 

23. 

30 

24 

.66 

23. 

40 

24 

.56 

23. 

51 

34 

35 

25 

.60 

23. 

87 

25.49 

23. 

93 

25 

.39 

24. 

09 

25 

.28 

24. 

20 

35 

36 

26 

.33 

24. 

55 

26.22 

24. 

67 

26 

.11 

24. 

78 

26 

.01 

24. 

89 

36 

37 

27 

.06 

25. 

23 

26.95 

25. 

35 

26 

.84 

25. 

47 

26 

.73 

25. 

59 

37 

38 

27 

.79 

25. 

92 

27.68 

26. 

04 

27 

.56 

26. 

16 

27 

.45 

26. 

23 

38 

39 

23 

.52 

26. 

60 

28.41 

26. 

72 

28 

.29 

26. 

85 

28 

.17 

26. 

97 

39 

40 

29 

.25 

27. 

23 

29.13 

27. 

41 

29 

.01 

27. 

53 

28 

.89 

27. 

66 

40 

41 

29 

.99 

27. 

96 

29.86 

28. 

09 

29 

.74 

28. 

22 

29 

.62 

28. 

35 

41 

42 

30 

.72 

28. 

64 

30.59 

23. 

78 

30 

.47 

28. 

91 

30 

.34 

29. 

04 

42 

43 

31 

.45 

29. 

33 

31.32 

29. 

46 

31 

.19 

29. 

60 

31 

.06 

29. 

74 

43 

44 

32 

.18 

30. 

01 

32.05 

30. 

15 

31 

.92 

30. 

29 . 

31 

. 7S 

30. 

43 

44 

45 

32 

.91 

30. 

69 

32.78 

30. 

33 

32 

.64 

30. 

98 

32 

.51 

31. 

12 

45 

46 

33 

.64 

31. 

37 

33.51 

31. 

52 

33 

.37 

31. 

66 

33 

.23 

31. 

81 

46 

47 

34 

.37 

32. 

05 

34.23 

32. 

20 

34 

.09 

32. 

35 

33 

.95 

32 

50 

47 

48 

35 

.10 

32. 

74 

34.96 

32. 

89 

34 

.82 

33. 

04 

34 

.67 

33 

19 

i 48 

49 

35 

.84 

33. 

42 

35.69 

33. 

57 

35 

.54 

33 

73 

35 

.40 

33 

83 

49 

50 

36 

.57 

34. 

10 

36.42 

34. 

26 

3G 

.27 

34. 

42 

36 

*12 

34 

58 

50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

d 

o 

c 

cJ 

5 

47 Deg. 

4G| Deg. 

46£ Deg. 

461 Deg. 
































































































TRAVERSE TABLE. 


89 


o 

• 

w 

c* 

p 

43 Deg. 

43$ Deg. 

431 Deg. 

43$ 

Deg. 

• 

C/I 

£3 

o 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dop. 

Lat, 

Dep. 

o 

p 

51 

37.30 

34.78 

37.15 

34.04 

30.99 

35.11 

36.84 

35.27 

ITi 

52 

38.03 

35.46 

37.88 

35.63 

37.72 

35.79 

37.56 

35.96 

52 

53 

38.76 

36.15 

38.60 

30.31 

38.44 

36.48 

38.29 

36.65 

53 

51 

39.49 

36. S3 

39.33 

37.00 

39.17 

37.17 

39.01 

37.34 

54 

55 

40.22 

37.51 

40.06 

37.69 

39.90 

37.86 

39.73 

38.03 

55 

56 

40.96 

38.19 

40.79 

38.37 

40.62 

38.55 

40.45* 

38.72 

50 

57 

!41.69 

38.87 

41.52 

39.06 

41.35 

39.24 

41.17 

39.42 

57 

58 

;42.42 

39.56 

42.25 

39.74 

42.07 

39.92 

41.90 

40. I l 

58 

59 

43.15 

40.24 

42.97 

40.43 

42.80 

40.61 

42.62 

40.80 

59 

60 

43.88 

40.92 

43.70 

41.11 

43.52 

41 .30 

43.34 

41.49 

60 

01 

44.61 

41.60 

44.43 

41.80 

44.25 

41.99 

44.06 

42.18 

61 

02 

45.34 

42.28 

45.16 

42.48 

44.97 

42.68 

44.79 

42.87 

62 

63 

46.08 

42.97 

45.89 

43.17 

45.70 

43.37 

45.51 

43.57 

63 

64 

46.81 

43.65 

40.62 

43.85 

46.42 

44.05 

46.23 

44.20 

64 

65 

47.54 

44.33 

47.34 

44.54 

47.15 

44.74 

46.95 

44.95 

65 

66 

4S.27 

45.01 

48.07 

45.22 

47.87 

45.43 

47.68 

45.64 

66 

67 

49.00 

45.69 

48.80 

45.91 

48.60 

46.12 

48.40 

46.33 

67 

68 

49.73 

46.3S 

49.53 

46.59 

49.33 

40.81 

49.12 

47.02 

68 

69 

50.46 

47.00 

50.26 

47.28 

50.05 

47.50 

49.84 

47.71 

69 

70 

51.19 

47.74 

50.99 

47.96 

50.78 

48.18 

50.57 

48.41 

70 

71 

51.93 

48.42 

51.71 

43.65 

51.50 

48.87 

51.29 

49.10 

71 

72 

52.66 

49.10 

52.44 

49.33 

52.23 

49.56 

52.01 

49.79 

72 

73 

53.39 

49.79 

53.17 

50.02 

52.95 

50.25 

52.73 

50.48 

73 

74 

54.12 

50.47 

53.90 

50.70 

53.08 

50.94 

53.45 

51.17 

74 

75 

54.85 

51.15 

54.63 

51.39 

54.40 

51.63 

54.18 

51.86 

75 

76 

55.58 

51.83 

55.36 

52.07 

55.13 

52.31 

54.90 

52.55 

76 

77 

50.31 

52.51 

56.08 

52.76 

55.85 

53.00 

55.62 

53.25 

77 

78 

57.05 

53.20 

50.81 

53.44 

56.58 

53.69 

56.34 

53.94 

78 

79 

57.78 

53.88 

57.54 

54.13 

57.30 

54.38 

I 57.07 

54.63 

79 

80 

58.51 

54.56 

58.27 

54.81 

58.03 

55.07 

I 57.79 

55.32 

80 

81 

59.24 

55.24 

59.00 

55.50 

58.70 

55.76 

58.51 

56.01 

81 

82 

59.97 

55.92 

59.73 

50.18 

59.48 

56.45 

59.23 

56.70 

82 

83 

60.70 

50.61 

60.45 

56.87 

60.21 

57.13 

59.96 

57.40 

S3 

84 

61.43 

57.29 

61.18 

57.56 

60.93 

57.82 

60.68 

58.09 

84 

85 

62.17 

57.97 

61.91 

58.24 

61.60 

58,51 

61.40 

58.78 

85 

88 

62.90 

58.65 

62.64 

58.93 

62.38 

59.20 

62.12 

59.47 

86 

87 

63.63 

59.33 

63.37 

59.61 

63.11 

59.89 

62.85 

60.16 

87 

88 

64.36 

60.02 

64.10 

60.30 

63.83 

60.58 

63.57 

00.85 

88 

89 

65.09 

60.70 

64.82 

60.98 

64.56 

61.26 

64.29 

61.54 

89 

90 

65.82 

61 .38 

65.55 

61.67 

65.28 

61.95 

65.01 

62.24 

90 

91 

66.55 

62.06 

66.28 

62.35 

66.01 

62.64 

65.74 

G2.93 

91 

92 

07.28 

02.74 

67.01 

63.04 

66.73 

63.33 

‘66.46 

03.62 

92 

93 

68.02 

63.43 

67.74 

63.72 

67.46 

64.02 

67.18 

64.31 

93 

94 

68.75 

64.11 

68.47 

64.41 

68.19 

64.71 

07.90 

65.00 

94 

95 

69.48 

64.79 

09.20 

65.09 

68.91 

65.39 

68.62 

65.69 

95 

96 

70.21 | 

65.47 

69.92 

65.78 

69.64 

66.08 

69.35 

60.39 

96 

97 

70.94 

66.15 

70.65 

60.46 

70.36 

66.77 

70.07 

67.08 

97 

98 

71.67 

66.84 

71.37 

67.15 

71.09 

67.46 

70.79 

67.77 

98 

99 

72.40 

67.52 

72.11 

67.83 

71.81 

68.15 

71.51 

63.46 ! 

99 

100 

73.14 

63.20 

72.84 

63.52 

72.54 

68.84 

72.24 

69.15 ' 

100 

d 

o 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

cd 

■*-* 

3 

47 Deg. 

1' 

46f Deg. 

46|- Deg. 

46$ Deg. 









































































































90 


TRAVERSE TABLE. 


4-i D eg. 


Lat. 


Dcp. 


1 

0 

72 

0 

.69 

2 

1 

.44 

1 

.39 

3 

2 

1G 

2 

.08 

4 

2 

88 

9 

/V 

.78 

5 

3 

60 

3 

.47 

6 

4 

32 

4 

.17 

7 

5 

04 

4 

. 86 

8 

5 

75 

5 

.56 

9 

6 

47 

6 

.25 

10 

/ 

19 

6 

. 95 

11 

7 

91 

7 

.64 

12 

8 

63 

8 

.04 

13 

9 

35 

9 

.03 

14 

10 

07 

9 

.73 

15 

10 

79| 10 

.42 

16 

11 

51 

11 

.11 

17 

12 

23 

1 1 

.81 

18 

12 

95 

12 

.50 

19 

13 

67 

13 

.20 

20 

14 

39(18 

.89 

21 

15 

11 

14 

.59 

22 

15 

83 

15 

.28 

23 

16 

54 

15 

.98 

24|l7 

26 

10 

.67 

25117 

98 

17 

.37 


70 18 
42 18 


20118 

27 19 

28 20.14110 
29(20 
30 21 


80120 
58 20 


.76 

.45 

.15 

.84 


32 23 

33 23- 
34124.46 
35(25. 18 
36 2 


.30 21 
.02 22 
. 74l22 


53 


37120 

38 27 

39 (28 

40 j 28, 
411*29 
42:30 
43(30 
44131 
45132 
46 33 


90 25 
62 25 
33 


05 
77 
4 9 28 


°1 


92 
23.62 
24.31 
01 
70 
40 
09 
79 


26. 

27. 

27. 


29 


47 

48 


33. 

34. 


49 35 


93 j 29 
65130 
37 31 
09 31 
.81 
, 53 
, 25 


33 

34 


50 35.97 34 


F « 

t v 

G 

' rt 

7 


Dop. 


:4S 
IS 
87 
,56 
.26 
,95 
, 05 
. 34 
,04 
,73 


Lat. 


46 Deg. 


44 \ Deg. 

1 

44^ Deg. 

44 4 - Deg. 

45 Deg 

*P- 

Distance. | 

Lat. 

Dep. 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dt 

1 0 

.72 

0 

.70 

0 

.71 

0. 

70 

0. 

71 

0. 

711 

0 

71 

0. 

71 

1 

1 

.43 

1 

.40 

1 

.43 

1. 

40 

1 . 

42 

1 . 

41 

1 

41 

1 

41 

2 

2 

.15 

2 

.09 

2 

.14 

2 . 

10 

2 . 

13 

2 . 

111 

2 

12 

2 . 

12 

3 

2 

.87 

2 

.79 

2 

.85 

2 . 

80 

2 . 

84 

2 

82' 

2 . 

S3 

2 . 

83 

4 

3 

.58 

3 

.49 

o 

«> 

.57 

3. 

50 

3. 

55 

3. 

52! 

3 . 

54 

O 

O 4 

54 

5 

4 

.30 

4 

. 19 

4 

.28 

4. 

21 

4. 

26 

4. 

22! 

4 . 

24 

4. 

24 

6 

5 

.01 

4 

.88 

4 

.99 

4. 

91 

4. 

97 

4. 

93 

4 . 

95 

4. 

95 


5 

.73 

5 

.58 

5 

.71 

5. 

61 

5. 

68 

5. 

63; 

5 . 

66 

5. 

66 

8 

6 

.45 

G 

.28 

6 

.42 

6. 

31 

6. 

39 

G. 

34 

6. 

36 

6. 

36 

9 

ry 

i 

.16 

6 

.98 

7 

.13 

7. 

01 

7. 

10 

7. 

04 

7. 

07 

7 • 

07 

10 

7 

.88 

7 

.68 

7 

.85 

7. 

71 

7 . 

81 

7. 

74 

7. 

78 

7 . 

78 

11 

8 

.60 

8 

.37 

8 

.56 

8. 

41 

8. 

52 

8. 

45 

8. 

49 

8. 

49 

J 2 

9 

.31 

9 

.07 

9 

.27 

9. 

11 

9. 

23 

9. 

15 

9. 

19 

9. 

19 

13 

10 

.03 

9 

77 

9 

.99 

9. 

81 

9. 

94 

9. 

86 

9. 

90 

9. 

90l 

14 

10 

.74 

10 

.47 

10 

.70 

10. 

51 

10. 

65 

10. 

56 

10. 

61 

10. 

61 

15 

11 

.46 

11 

.16 

11 

.41 

11. 

21 

11. 

36 

li. 

26 

11. 

31 

11 . 

31 

16 

12 

.18 

1 1 

.86 

12 

13 

11. 

92 

12. 

07 

11. 

97 

12. 

02 

12. 

02 

17 

12 

.89 

12 

56 112 

.84 

12. 

62 

12. 

78 

12. 

67: 

12. 

73 

12. 

73 

18 

13 

.61 

13 

Of-| i 

A/ v.’ 

13 

.55 

13. 

321 

13. 

49 

13. 

33 

13. 

43 

13. 

43 

19 

14 

.33 

13 

.96 

14 

.26 

14. 

021 

14. 

20 

14. 

08 

14. 

14 

14. 

14 

20 

15 

.04 

14 

65 

14 

.98114 

72!! 14. 

91 

14. 

7SI 

14. 

85 

14. 

85 

21 

15 

.76 

15 

.35 

15 

.69 

15. 

42 

15. 

62 

15. 

49! 

15. 

56 

15. 

56 

22 

16 

.47 

16 

.05 

16 

.40 

16. 

12 

16. 

33 

16. 

19 

16. 

26 

16. 

26 

23 

17 

.19 

16 

751 

17 

.12 

16. 

82 

17. 

04 

16. 

90 

16. 

97 

16. 

97 

24 

17 

.9! 

17 

.441 

17 

.83 

17. 

52 

17. 

75 

17. 

60 

17. 

68 

17. 

68 

25 

18 

.62 

18 

.14 

18 

.54 

18. 

221,18. 

46 

18. 

30 

18. 

38 

18. 

38 

26 

19 

.34 

18 

.84! 

19 

.26 

18. 

921 

19. 

17 

19. 

01 

19. 

09 

19. 

09 

27 

20 

.06 

19 

54j 

19 

.97 

19. 

63’ 

19. 

89 

19. 

71 

19. 

80 

19. 

80 28 

20 

.77 

20 

.24 

20 

.63 

20. 

33 

20. 

60 

0. 

42 

20. 

51 

20. 

51 

29 

21 

.49 

20 

.93 

21 

. 

.40 

21 

03i 

21 . 

31 

21. 

12 

21. 

21 

21. 

21 

30 

22 

.21 

21 

.63 

22 

.11 

21. 

73 

,22. 

02 

21. 

82 

21. 

92 

21. 

92 

31 

22 

.92 

22 

.33; 

22 

.82 

22. 

43 

22. 

73 

22. 

53 

A* Ai 

63 

22. 

03 

32 

23 

.64 

23 

.03 

23 

.54 

23. 

13 

23. 

44 

23. 

23 

23. 

33 

23. 

33 

33 

24 

.35 

23 

.72 

24 

.25 

23. 

83 

24. 

15123. 

94 

24 

04 

24. 

04 

34 

25 

.07 

24 

.42 

24 

.96 

24. 

53 

24. 

36 

24. 

G4| 

24. 

75124. 

75 

35 

25 

.79 

25 

. 12 

25 

.68 

*y ^ 

23 

25. 

57 

25. 

34 i 

25. 

46 

25. 

46 

36 

26 

.50 

25 

.82 

26 

.39 

25 

93 

26 

28 

26. 

05 

26 

16 

26. 

16 

37 

27 

.22 

26 

<v> 

• ly.v 

27 

. 10 

26 

63 

26. 

99 

26. 

75 

26 

87 

26 

87 

38 

27 

.94 

27 

.21 

27 

.82 

27 

34 

27. 

70 

27. 

46 

27 

58 

27 

58 

39 

28 

.65|27 

.91 

28 

. 53 

,28 

04 

28 

41 

28. 

16 

28 

28 

28 

28 

40 

29 

.37 

28 

.61 

29 

.24 

28 

74 

29 

12 

2S 

86 

28 

.99 

28 

99 

41 

30 

.08 

29 

.31 

29 

.96 

29 

44 

29 

83 

29 

57 

29 

.70 

29 

70 

42 

30 

.80 

30 

.00; 

30 

. 67 

30 

14 

30 

54 

30 

27 

30 

.41 

30 

41 

43 

31 

.52 

30 

.70; 

31 

.38 30 

84 

31 

25 

30 

.93 

31 

.11 

31 

.11 

44 

32 

.23 

31 

.40 

32 

.10 

31 

54 

31 

.96 

31 

.68 

31 

.82 31 

.82 

45 

32 

.95 

32 

.10| 

32 

.81 

32 

24 

32 

67 

32 

.38 

32 

.53,32 

.53 

46 

33 

.67 

.32 

.80; 

33 

.52 

32 

94 

33 

38 

33 

.09 

133 

• 23| 33 

.23 

'47 

34 

.08 

33 

• 49 

31 

.24 

33 

64 

!34 

.09133 

.79 

33 

.94133 

.94148 

35 

.10 

34 

.19 

34 

. 95 

34 

.34 

34 

.80 34 

. 50 

34 

.65 

34 

.65 

49 

50 

35 

.82 

'34 

.89 

35 

.66 

35 

05 

35 

.51 

35 

.20 

35 

.36 

35 

.36 

D 

4 

ep. 

Lat. 

Dep. 

1 

•t. 

Dep. 

Lat. 

Dcp. 

|l 

at. 

r . 

j Distance. 

L 

5f Deg. 

45i Deg. 

45J De 

1 


i 45 Deg 

c 























































































































































TKAVV.USE TABLK. 


01 


a 

►— • 

w 

r-*" i 

P> I._ 

g ! Lai. 


41 Deg. 


51 33 
< 52 37 


Dep. 


. 69 35.43 
.41 36. 12 
53133.12 33.82 
84 37.51 
50 33.21 


>•) 39, 
40, 


56 

57 

58 


41 
41 
59 42 
00 43 

61 
62 
63 


00 39.601 
72 40. 

44 40.931 
16 41.63 


43, 

44, 

45, 
64 46, 


65 

66 

67 

68 

69 

70 

71 

72 

73 


46 

47 

48 
43 

49 

50 


88 

60 

32 

04 

76 

48 


o 1 

51 

52 


74 53 

75 53 


54 

55 

56 

56 

57 


42.37 
43.07 
43.76 
44.46 
45. 15 
45.85 
.20146.54 
, 92147.24 
,63:47.93 
.35:43.63 

, 07|49.32 
,79; 50.02 
,51150.71 
.23 51.40 
,95 52.10 
.67 52.79 
,39 53.49 
.11 54.18 
,83154.88 


76 

77 

78 

79 

80 

81 58.27156.27 

82 53.99 56.90 


83! 59 
84 60 
85161 


.71157.66 
.42 58.35 
. 14 59.05 
88'61 .86 59.74 


87162 
83163 
89 64 
90; 64 

Til 65 
92 66 
93166 
94; 67 
95! 68 

96 69 

97 69 
98170 
99 71 


.58 60.44 
.30 61.13 
.02 61.82 
.74 62.52 
.46 63.21 
.18 63.9! 

. 90 64.60 
. 62 65.30 
.34 65.99 


100 


O 


n 


.78 67.38 
.50 68.08 
.21 63.77 
7 1.93 69.47 

Dep. Lat. 


46 Deg. 


1 

j 44 i 

1 

i u-g. 

44i Deg. 

44| 

t)e £- , 

1 

45 Deg. 

Distance. | 

j Lat. 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

'36.53 

35.59 

36.33 35.75 

36.22 

35.90 

38.06 

36.06j 

51 

37.25 

35.29 

37.09(36.45 

36.93 

36.61 

36.77 

38.77 

52 

37.96 

36.98 

37.30 

37.15 

37.64 

37.31 

37.48 

37.48 

53 

33.63 

37.68 

33.52 

37.85 

33.35 

33.02 

38.18 

38.18 

54 

39.40 

38.33 

39.23 

38.55 

39.06 

38.72 

38.89 

38.89 

55 

10.11 

39.08 39.94 39.25 

39.77 

39.42 

39.60 

39.60 

50 

10.83 

39.77, 

40.66 

39.95 

40.48 

40.13 

40.3! 

40.31 

57 

41.55 

40.47 

41.37 

40.65 

41.19 

40.83 

41.01 

41.01 

58 

4-2.26 

41.17 

42.03 

41.35 

41.90 

41.54 

41.72 

4 1.72 

59 

42.98 

41.87 

42.79 

42.05 

42.61 

42.24! 

42.43 

4-2.43 j 

60 

43.69 

42.57 

43 51 

42.76 

43.32 

42.941(43.13 43.13 

61 

44.41 

43.26 

44.22 

43.46 

44.03 

43.65:43.84 

43.84 

62 

145.13 

43.96 

44.93 

44.16 

44.74 

44.35 

44.55 

44.55 

03 

45.84 

44.66 

45.65 

44.86 

45.45 

45.06 

45.25 

45.25 

04 

46.56 

45.36 

46 36 

45.56 

46.16 

45.76! 

45.96,45.96 

65 

(47.28 

46.05 

47.07 

48.26 

48.87 

46.46 

46.67 

46.07 

66 

147.99 

46.75 

47.79 

46.96 

47.58 

47.17 

47.38 

47.38 

67 

(48.71 47.45 

48.50 

47.66 

43.29 

47.87 

43.08 

48.08 

53 

49.42 

48.15 

49.21 

48.36 

49.00 

48.58 

48.79 

48.79 

69 

50.14 

48.85 

49.93 

49.06 

49.71 

49.28 

49.50 

49.50 

70 

(50.86 

49.54 

(50.64 

49.76 

50.42 

49.93 

50.20 

50.20 

71 

51.57 

50.24 

; 51.35 

50.47} 

51.13 50.69 

50.91 50.91 

72 

(52.29 

50.94 

52.07 

51.17 

51.84 51.39 

51.62 

51.62 

73 

53.01 

51.64 

52.78 

5 i .87 

*52.55 52.10 

52.33 52.33 

74 

153.72 

52.33 

53.49 

52.57 

53.26 

52.80 

53.03 53.03 

75 

54.44 

53.03 

54.21 

53.27 

53.97 

53.51 

53.74! 53.74 

76 

55.16 

53.731 

54.92 

>53.97 

54.68 

54.21 

54.45(54.45 

77 

55.87 

54.43J 

55.63 

54.67 

55.39154.91 

55.15(55.15 

78 

56.59 

55.13 

56.35 

55.37 

56.10 

55.62 

55.86155.80 

79 

57.30 

55.82 

57.06 

56.07 

(56.81 

56.32 

56.57 

56.57 

SO 

58.02 

56.52 

57.77 

56.77 

57.52 57.03 

57.28157.28 

81 

:58.74 

57.22 

58.49 

57.47 

58.24157.73 

57.98157.98 

82 

I 59.45 

57.92 

59.20 

58.18 

58.95158.43 

58.69! 58.69 

83 

|C0. 17 

58.61 

59.91 

58.83 

59.66(59.14 

59.40159.40 

84 

60.89 

59.31 

60.63 

59.58 

60.37(59.84 

60.10160.10 

88 

61.60 

60.0! 

6 l. 31 

60.28 

61.08 60.55 

60.81 60.81 

86 

62.32 

60.71 

62.05 

60.98 

61.79 G1.25 

61.52 61.52 

87 

1163.03 

61.41 

62.77 

6! .68 

62.60 61.95 

62.23 1 '62.23 

88 

163.75 

62.10 

63.48 

62.33 

63.21 62.66 

62.93 

62.93 

89 

164.47 

62.80 

64.19 

63.08 

63.92 63.36 

63.64 

03.64 

90 

(65.18 

63.50 

64.91 

63.78 

64.63164.07 

64.35 

64.35 

91 

65.90 

64.20 

05.62 

64.48 

165.34 

64.77 

65.05 

65.05 

92 

66.62 

64.89 

66.33 

65.13 

(66.05 

65.47 

65.76 

65.70 

93 

67.33 

65.59 

67.05 

65.89 

66.76 

66.18 

06.47 

06.47 

94 

68.05 

66.29 

67.78 

66.59 

67.47 

06.88 

07.18167.18 

95 

163.76 

66.99 

68.47 

67.29 

68.18 

67.59 

67.88(67. S3 

96 

1169.48 

67.69 

69.19 

67.99 

68.89'68.29 

68.59(08.59 

97 

70.20 68.38 

69.90 

68.69 

69.60 

68.99 

09.30 69.30 

93 

70.91 

69.03 

70.61 

69.39 

70.31 

69.70 

70.00,70.00 

99 p 

71.63 

69.78 

71.33 

70.09 

71.02 

70.40 

70.71 

70.71 

100 | 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

6 \ 

0 

c 

A r 3 

Deg. 

45 h Deg. 

45J Deg. 

45 Deg. 

i 

-4-J 1 

Vi 












































































































































92 


A TABLE OF RHUMBS. 

SHOWING 


TIIE DEGREES, MINUTES, AND SECONDS, THAT EVERY POINT AND QUARTER 

POINT OF TIIE COMPASS MAKES WITH 
THE MERIDIAN. 


NORTH. 

|Pts. 

qr 

o 

/ 

// 

1 Pts. 

q* 

SOUTH. 



0 

1 

2 

48 

45 

0 

1 





1 

2 

5 

37 

30 

0 

2 





0 

3 

8 

26 

15 

0 

3 



N by E. 

N. by W. 

1 

0 

11 

15 

0 

1 

0 

S. by E. 

S. by W. 



1 

1 

14 

3 

45 

1 

1 





1 

2 

i G 

52 

30 

1 

2 





1 

3 

J 9 

41 

15 

1 

3 



N.N.E. 

N.N.W. 

2 

0 

22 

30 

0 

2 

0 

S.S.E. 

S.S.W. 



2 

1 

25 

18 

45 

2 

1 





2 

2 

28 

7 

30 

2 

2 



N.E. by N. 


2 

3 

30 

53 

15 

2 

3 



N.W. by N. 

3 

0 

33 

45 

0 

3 

0 

S.E. by S. 

S.W. by S. 



3 

1 

31 

33 

45 

3 

1 





3 

2 

30 

22 

30 

3 

2 





3 

3 

42 

11 

15 

3 

3 



N.E. 

N.W. 

4 

0 

45 

0 

0 

4 

0 

S.E. 

s.w. 



4 

1 

47 

48 

45 

4 

1 





4 

2 

50 

37 

30 

4 

2 



N.E. by E. 


4 

3 

53 

25 

15 

4 

3 



N.W.by W. 

5 

0 

5G 

15 

0 

5 

0 

S.E. byE. 

S.W. by W. 



5 

1 

59 

3 

45 

5 

1 





5 

2 

61 

52 

30 

5 

2 





5 

3 

64 

41 

15 

5 

3 



E.N.E. 

W.N W. 

6 

0 

67 

30 

0 

6 

0 

E.S.E. 

w s.w 



G 

1 

70 

18 

45 

6 

1 





G 

2 

73 

7 

30 

6 

2 





6 

3 

75 

56 

15 

6 

3 1 



E. by N. 

W. by N. 

7 

0 

78 

45 

0 

7 

0 

E. by S. 

W. by S. 



7 

1 

81 

33 

45 

7 

1 





7 

2 

84 

22 

30 

7 

2 



East. 


7 

3 

87 

11 

15 

7 

3 



West. 

8 

0 

90 

0 

0 

8 

0 

East. 

West 



































workman’s table, for correcting the middle latitude. 93 


Mid. 1 


Lat. 


30 

I 

40 


50 


60 

| 

70 


80 


90 


TOO 


HO 

o 

c 

' 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

15 

0 

02 

0 

03 

0 

04 

0 

06 

0 

09 

0 

12 

0 

15 

0 

19 

0 

23 

1G 

0 

02 

0 

03 

0 

04 

0 

06 

0 

09 

0 

12 

0 

15 

0 

18 

0 

22 

17 

0 

02 

0 

03 

0 

04 

0 

06 

0 

08 

0 

11 

0 

14 

0 

17 

0 

21 

IS 

0 

02 

0 

03 

0 

04 

0 

06 

0 

08 

0 

11 

0 

14 

0 

17 

0 

20 

19 

0 

02 

0 

03 

0 

04 

0 

06 

0 

07 

0 

10 

0 

13 

0 

16 

0 

19 

23 

0 

02 

0 

03 

0 

C4 

0 

00 

0 

07 

0 

09 

0 

12 

0 

15 

0 

18 

21 

0 

02 

0 

03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

18 

22 

0 

02 

0 

03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

17 

22 

0 

02 

0 

03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

17 

24 

0 

02 

0 

03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

25 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

2G 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

27 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

08 

0 

11 

0 

14 

0 

16 

23 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

29 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

30 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

31 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

32 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

33 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

34 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

35 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

36 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

37 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

38 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

39 

0 

C2 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

40 

0 

02 

0 

03 

0 

04 

0 

05 

0 

08 

0 

08 

0 

10 

0 

13 

0 

15 

41 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

42 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

43 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

44 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

45 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

46 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

47 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

48 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

49 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

17 

50 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

17 

51 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

17 

52 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

12 

0 

15 

0 

18 

53 

0 

02 

0 

03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

18 

54 

0 

02 

0 

03 

O' 

04 

0 

06 

0 

08 

0 

10 

0 

13 

0 

16 

0 

19 

55 

0 

02 

0 

03 

0 

04 

0 

06 

0 

03 

0 

10 

0 

13 

0 

16 

0 

19 

56 

0 

02 

0 

03 

0 

04 

0 

06 

0 

08 

0 

10 

0 

13 

0 

16 

0 

20 

57 

0 

02 

0 

03 

0 

04 

0 

06 

0 

08 

0 

11 

0 

14 

0 

17 

0 

20 

58 

0 

02 

0 

03 

0 

04 

0 

06 

0 

09 

0 

11 

0 

14 

0 

17 

0 

21 

59 

0 

02 

0 

03 

0 

04 

0 

06 

0 

09 

0 

12 

0 

15 

0 

18 

0 

22 

60 

0 

02 

0 

03 

0 

04 

0 

06 

0 

09 

0 

12 

0 

15 

0 

19 

0 

23 

61 

0 

02 

0 

03 

0 

05 

0 

07 

0 

09 

0 

12 

0 

15 

0 

19 

0 

23 

62 

0 

02 

0 

03 

0 

05 

0 

07 

0 

09 

0 

12 

0 

16 

0 

20 

0 

24 

63' 

0 

02 

0 

04 

0 

05 

0 

07 

0 

09 

0 

13 

0 

18 

0 

20 

0 

24 

64 

0 

02 

0 

04 

0 

06 

0 

08 

0 

09 

0 

13 

0 

17 

0 

21 

0 

25 

65 

0 

02 

0 

04 

0 

06 

0 

08 

0 

10 

0 

13 

0 

17 

0 

21 

0 

25 

66 

0 

02 

0 

04 

0 

06 

0 

08 

0 

10 

0 

14 

0 

18 

0 

22 

0 

26 

67 

0 

02 

0 

04 

0 

06 

0 

08 

0 

11 

0 

15 

0 

18 

0 

23 

0 

27 

68 

0 

02 

0 

04 

0 

06 

0 

08 

0 

11 

0 

15 

0 

19 

0 

24 

0 

2 S 

69 

0 

02 

0 

05 

0 

06 

0 

09 

0 

12 

0 

16 

0 

£0 

0 

25 

0 

30 

70 

0 

03 

0 

05 

0 

06 

0 

09 

0 

13 

0 

17 

0 

21 

0 

26 

0 

31 

71 

0 

04 

0 

06 

0 

07 

0 

09 

0 

13 

0 

18 

0 

22 

0 

27 

0 

33 

72 1 

0 

04 

0 

06 

0 

08 

0 

10 

0 

14 

0 

19 

0 

23 

0 

29 

0 

35 


I m **•••- wnuoBWWi 


f 


25 






































94 WORKMAN’S TABLE, FOR CORRECTING THE MIDDLE LATITUDE. 


Mid. 

J Lat. 

120 

1 130 

140 

150 

160 

i 170 

ISO 

190 

200 

o 

15 

o / 

o / 

o / 

o / 

o / 

o / 

o / 

O / 

o / ; 

0 27 

0 31 

0 35 

0 40 

0 45 

0 51 

0 58 

1 G6 

1 14 

16 

0 26 

0 30 

0 34 

0 38 

0 43 

0 49 

0 56 

1 03 

1 11 

17 

0 25 

0 28 

0 32 

0 37 

0 42 

0 48 

0 54 

1 01 

1 03 

18 

0 24 

0 27 

0 31 

0 36 

0 41 

0 46 

0 52 

0 58 

1 06 

19 

0 23 

0 26 

0 30 

0 34 

0 40 

0 45 

0 50 

0 56 

1 03 

20 

0 22 

0 25 

0 29 

0 33 

0 38 

0 43 

0 48 

0 54 

1 00 

21 

0 21 

0 25 

0 29 

0 33 

0 37 

0 42 

0 47 

0 53 

0 58 


0 20 

0 24 

0 23 

0 32 

0 36 

0 41 

0 46 

0 51 

0 56 

23 

0 20 

0 24 

0 28 

0 32 

0 36 

0 40 

0 45 

0 50 

0 55 J 

24 

0 19 

0 23 

0 27 

0 31 

0 35 

0 39 

0 44 

0 48 

0 53 

25 

0 19 

0 23 

0 27 

0 31 

0 35 

0 39 

0 43 

0 47 

0 52 

26 

0 19 

0 22 

0 26 

0 30 

0 34 

0 33 

0 42 

0 47 

0 52 

27 

0 19 

0 22 

0 26 

0 30 

0 33 

0 33 

0 42 

0 46 

0 51 

28 

0 18 

0 21 

0 25 

0 29 

0 33 

0 37 

0 41 

0 46 

0 51 

29 

0 18 

0 21 

0 25 

0 29 

0 32 

0 36 

0 41 

0 45 

0 50 

30 

0 18 

0 21 

0 25 

0 28 

0 32 

0 36 

0 41 

0 45 

0 50 

31 

0 18 

0 21 

0 25 

0 23 

0 32 

0 36 

0 41 

0 45 

0 50 

32 

0 18 

0 21 

0 25 

0 28 

0 31 

0 36 

0 41 

0 45 

0 50 

33 

0 18 

0 21 

0 24 

0 27 

0 31 

0 35 

0 40 

0 44 

0 49 

34 

0 18 

0 21 

0 24 

0 27 

0 31 

0 35 

0 40 

0 44 

0 49 

35 

0 18 

0 21 

0 24 

0 27 

0 31 

0 35 

0 40 

0 44 

0 49 

36 

0 18 

0 21 

0 24 

0 27 

0 31 

0 35 

0 40 

0 44 

0 49 

37 

0 18 

0 21 

0 24 

0 27 

0 31 

0 35 

0 40 

0 44 

0 49 

38 

0 18 

0 21 

0 24 

0 27 

0 31 

0 36 

0 40 

0 45 

0 50 

39 

0 18 

0 21 

0 25 

0 28 

0 32 

0 36 

0 41 

0 45 

0 50 

40 

0 18 

0 22 

0 25 

0 28 

0 32 

0 36 

0 41 

0 45 

0 50 

41 

0 18 

0 22 

0 25 

0 28 

0 32 

0 37 

0 41 

0 45 

0 50 

42 

0 18 

0 22 

0 26 

0 29 

0 33 

0 37 

0 42 

0 46 

0 51 

43 

0 19 

0 23 

0 26 

0 30 

0 34 

0 38 

0 42 

0 46 

0 51 

44 

0 19 

0 23 

0 27 

0 30 

0 34 

0 38 

0 43 

0 47 

0 52 S 

45 

0 19 

0 23 

0 27 

0 31 

0 35 

0 39 

0 43 

0 47 

0 52 

46 

0 19 

0 23 

0 27 

0 31 

0 35 

0 39 

0 44 

0 43 

0 53 

47 

0 20 

0 23 

0 27 

0 31 

0 35 

0 40 

0 44 

0 49 

0 54 

48 

0 20 

0 23 

0 27 

0 31 

0 35 

0 40 

0 45 

0 50 

0 55 

49 

0 21 

0 24 

0 28 

0 32 

0 36 

0 41 

0 45 

0 51 

0 57 

50 

0 21 

0 24 

0 28 

0 32 

0 36 

0 41 

0 46 

0 52 

0 58 

51 

0 21 

0 24 

0 23 

0 32 

0 37 

0 42 

0 47 

0 53 

0 59 

52 

0 22 

0 25 

0 29 

0 33 

0 37 

0 42 

0 48 

0 54 

1 00 

53 

0 22 

0 25 

0 29 

0 33 

0 38 

0 43 

0 49 

0 55 

1 01 

54 

0 23 

0 26 

0 30 

0 34 

0 39 

0 44- 

0 50 

0 56 

1 02 

55 

0 23 

0 26 

0 30 

0 35 

0 40 

0 45 

0 51 

0 57 

1 03 

56 

0 24 

0 27 

0 31 

0 36 

0 41 

0 46 

0 52 

0 58 

1 04 

57 

0 24 

0 28 

0 32 

0 37 

0 42 

0 48 

0 54 

1 00 

1 06 

58 

0 25 

0 29 

0 33 

0 38 

0 44 

0 50 

0 55 

1 02 

1 08 

59 

0 26 

0 30 

0 34 

0 39 

0 45 

0 51 

0 57 

1 04 

1 10 

60 

0 27 

0 31 

0 35 

0 40 

0 46 

0 52 

0 59 

1 06 

1 13 

61 

0 27 

0 31 

0 36 

0 41 

0 47 

0 54 

1 01 

1 08 

1 15 

62 

0 28 

0 32 

0 37 

0 42 

0 49 

0 56 

1 03 

1 10 

1 18 

63 

0 29 

0 33 

0 39 

0 44 

0 51 

0 58 

1 05 

1 12 

1 21 

64 

0 29 

0 34 

0 40 

0 46 

0 53 

1 00 

1 07 

1 14 

1 24 

65 

0 30 

0 35 

0 41 

0 48 

0 55 

1 02 

1 09 

1 17 

1 27 

66 

0 31 

0 37 

0 43 

0 50 

0 58 

1 05 

1 12 

1 21 

1 31 

67 

0 33 

0 38 

0 45 

0 53 

1 00 

1 07 

1 16 

1 25 

1 35 

63 

0 34 

0 40 

0 48 

0 55 

1 02 

1 10 

1 19 

1 30 

1 39 

69 

0 36 

0 42 

0 50 

0 58 

1 05 

1 13 

1 23 

1 34 

1 44 j 

70 

0 38 

0 44 

0 52 

1 00 

1 08 

1 17 

1 23 

1 39 

1 50 

71 

0 40 

0 46 

0 55 

1 03 

1 12 

1 22 

1 32 

1 44 

1 56 | 

72 

0 42 

0 49 

0 58 

1 06 

1 16 

1 27 

1 38 

1 50 

L£iJ 

—■as.r-Ai*eu//s 









* 


% 

























































TABLE 

OF 

MERIDIONAL PARTS. 



95 

M. 

| 0O| I© 

20 1 30 ] 40 ] 501 Go] 70 1 80 | go] i(p| no] 120 

130 

0 

0 

GO 

120 

180 

240 

300 

361 

421 

482 

542 

603 

664 

725 

787 

1 

1 

G1 

121 

181 

241 

301 

362 

422 

483 

543 

604 

665 

723 

788 

o 

<%• 

o 

G2 

1 OO 

1 /V/V 

182 

242 

302 

363 

423 

484 

544 

605 

666 

727 

789 

3 

3 

63 

123 

183 

243 

303 

364 

424 

485 

545 

606 

667 

728 

790 

4 

4 

G4 

124 

184 

244 

304 

365 

425 

486 

546 

607 

668 

729 

791 

5 

5 

G5 

125 

185 

245 

305 

366 

426 

487 

547 

608 

669 

730 

792 

G 

6 

G6 

126 

186 

246 

306 

367 

427 

488 

548 

609 

670 

731 

793 

7 

7 

G7 

127 

187 

247 

307 

368 

428 

489 

549 

610 

671 

732 

794 

8 

8 

68 

128 

188 

248 

308 

369 

429 

490 

550 

611 

672 

734 

795 

9 

9 

69 

129 

189 

249 

309 

370 

430 

491 

551 

612 

673 

735 

796 

10 

10 

70 

130 

190 

250 

310 

371 

431 

492 

552 

613 

664 

738 

797 

11 

11 

71 

131 

191 

251 

311 

372 

432 

493 

553 

614 

675 

737 

798 

12 

12 

72 

132 

192 

252 

312 

373 

433 

494 

554 

615 

676 

738 

799 

! 13 

13 

73 

133 

193 

253 

313 

374 

434 

495 

555 

616 

677 

739 

800 

14 

14 

74 

134 

194 

254 

314 

375 

435 

498 

556 

617 

678 

740 

801 

S 15 

15 

75 

135 

195 

255 

315 

376 

436 

497 

557 

618 

679 

741 

802 

9 1G 

1G 

7G 

136 

196 

256 

316 

377 

437 

498 

558 

619 

680 

742 

803 

17 

17 

77 

137 

197 

257 

317 

378 

438 

499 

559 

620 

681 

743 

804 

18 

18 

78 

138 

198 

258 

318 

379 

439 

500 

560 

621 

682 

744 

805 

•19 

19 

79 

139 

199 

259 

319 

3S0 

440 

501 

561 

622 

683 

745 

808 

20 

20 

80 

140 

200 

260 

320 

381 

441 

502 

582 

623 

684 

746 

807 

21 

O 1 
A) i 

81 

141 

201 

201 

321 

382 

442 

503 

563 

624 

685 

747 

808 

22 

OO 

A/Aj 

82 

142 

202 

262 

322 

383 

443 

504 

564 

625 

687 

74S 

809 

23 

23 

83 

143 

203 

263 

323 

384 

444 

505 

565 

626 

68S 

749 

810 

1 24 

24 

84 

144 

204 

264 

324 

385 

445 

506 

567 

627 

639 

750 

811 

25 

25 

85 

145 

205 

265 

325 

386 

446 

507 

568 

628* 

690 

751 

812 

2G 

2G 

86 

146 

206 

266 

326 

387 

447 

508 

569 

629 

691 

752 

813 

27 

27 

87 

147 

207 

267 

327 

388 

448 

509 

570 

631 

692 

753 

815 

28 

28 

88 

148 

208 

268 

328 

389 

449 

510 

571 

632 

693 

754 

816 

29 

29 

89 

149 

209 

269 

330 

390 

450 

511 

572 

633 

694 

755 

817 

30 

30 

90 

150 

210 

270 

331 

391 

451 

512 

573 

634 

695 

756 

818 

31 

31 

91 

151 

211 

271 

332 

392 

452 

513 

574 

635 

696 

757 

819 

32 

32 

92 

152 

212 

272 

333 

393 

453 

514 

575 

636 

697 

758 

820 

33 

33 

93 

153 

213 

273 

334 

394 

454 

515 

576 

637 

698 

759 

821 

34 

34 

94 

154 

214 

274 

335 

395 

455 

516 

577 

638 

699 

760 

822 

35 

35 

95 

155 

215 

275 

336 

396 

456 

517 

578 

639 

700 

761 

823 

3G 

36 

96 

156 

216 

276 

337 

397 

457 

518 

579 

640 

701 

762 

824 

37 

37 

97 

157 

217 

277 

338 

398 

458 

519 

580 

641 

702 

763 

825 

38 

38 

98 

158 

218 

278 

339 

399 

459 

520 

581 

642 

703 

764 

826 

39 

39 

09 

159 

219 

279 

340 

400 

460 

521 

582 

643 

704 

765 

827 

!' 40 

40 

100 

160 

220 

280 

341 

401 

461 

522 

583 

644 

705 

768 

823 

41 

41 

101 

161 

221 

281 

342 

402 

462 

523 

584 

645 

706 

767 

829 

42 

42 

102 

162 

222 

282 

343 

403 

463 

524 

585 

646 

707 

768 

830 

43 

43 

103 

163 

223 

283 

344 

404 

464 

525 

586 

647 

70S 

769 

831 

44 

44 

104 

164 

224 

284 

345 

405 

465 

526 

587 

648 

709 

770 

832 

45 

45 

105 

165 

225 

285 

346 

406 

466 

527 

588 

649 

710 

771 

833 

46 

46 

106 

166 

226 

286 

347 

407 

467 

528 

589 

650 

.711 

772 

834 

47 

47 

107 

167 

227 

287 

348 

408 

46S 

529 

590 

651 

712 

773 

835 

48 

48 

108 

168 

228 

288 

349 

409 

469 

530 

591 

652 

713 

774 

836 

49 

49 

109 

169 

229 

289 

350 

410 

470 

531 

592 

653 

714 

775 

837 

50 

50 

110 

170 

230 

290 

351 

411 

471 

532 

593 

654 

0 715 

777 

838 

51 

51 

111 

171 

231 

291 

352 

412 

472 

533 

594 

655 

716 

778 

839 

52 

52 

112 

172 

232 

292 

353 

413 

473 

534 

595 

656 

717 

779 

840 

53 

53 

113 

173 

233 

293 

354 

414 

474 

535 

596 

657 

718 

' 780 

841 

54 

54 

114 

174 

234 

294 

355 

415 

476 

536 

597 

658 

719 

781 

842 

55 

55 

115 

175 

235 

295 

356 

416 

477 

537 

598 

659 

720 

782 

843 

56 

56 

116 

176 

236 

296 

357 

417 

478 

538 

599 

660 

721 

783 

844 

57 

57 

117 

177 

237 

297 

358 

418 

479 

539 

600 

661 

722 

784 

845 

58 

58 

118| 

178 

238 

293 

359 

419 

480 

540 

001 

662 

723 

785 

846 

591 

59 

1 ] 9| 

179 

239 

299 

360 

420 

481 

541 

602 

6G3 

724 

786 

847 





























































96 


TABLE OF MERIDIONAL PARTS. 


■■ ■ ,n, mw m urm-m ■ii w i"» i imiiP'i i n- 1 ■ m i ■■ i, i m n. nn iipii mu m .mu n nw ni-iiimrrrTr 

M. | 14Q| 150| 16°| 17Q| 18Q| 19Q| 2QQ| 21Q[ 22Q| 23Q| 24Q| 25Q| 26Q| 27° 


0 

848 

■910 

973 

1035 

1098 

1161 

1225 1289 

1354 

1419 

1484 

1550 

1616 

1684 

1 

850 

911 

974 

36 

99 

63 

26 

90 

55 

20 

85 

51 

18 

85 

2 

851 

913 

975 

37 

1100 

64 

27 

91 

56 

21 

86 

52 

19 

86 

3 

852 

914 

976 

38 

01 

65 

28 

92 

57 

22 

87 

53 

20 

87 

4 

853 

915 

977 

39 

02 

66 

29 

93 

58 

23 

83 

54 

21 

88 

5 

854 

916 

978 

41 

03 

67 

30 

95 

59 

24 

90 

56 

22 

89 

G 

855 

917 

979 

42 

05 

68 

32 

96 

60 

25 

91 

57 

23 

90 

7 

856 

918 

980 

43 

06 

69 

33 

97 

61 

26 

92 

58 

24 

91 

8 

857 

919 

981 

44 

07 

70 

34 

98 

62 

27 

93 

59 

25 

93 

9 

858 

920 

982 

45 

08 

71 

35 

99 

63 

28 

94 

60 

26 

94 

10 

859 

921 

983 

1046 

1109 

1172 

1236 

1300 

1364 

1430 

1495 

1561 

1628 

1695 

11 

860 

922 

984 

47 

10 

•73 

37 

01 

66 

31 

96 

62 

29 

96 

12 

861 

923 

985 

48 

11 

74 

38 

02 

67 

32 

97 

63 

30 

97 

13 

862 

924 

986 

49 

12 

75 

39 

03 

68 

33 

98 

64 

31 

98 

14 

863 

925 

987 

50 

13 

76 

40 

04 

69 

34 

99 

65 

32 

99 

15 

864 

926 

988 

51 

14 

77 

41 

05 

70 

' 35 

1500 

67 

33 

1700 

16 

865 

927 

989 

52 

15 

78 

42 

06 

71 

36 

02 

68 

34 

01 

17 

866 

928 

990 

53 

16 

79 

43 

07 

72 

37 

03 

69 

35 

03 

18 

867 

929 

991 

54 

17 

81 

44 

08 

73 

38 

04 

70 

37 

04 

19 

868 

930 

993 

55 

18 

82 

45 

10 

74 

39 

05 

71 

38 

05 

20 

869 

931 

994 

1056 

1119 

1183 

1246 

1311 

1375 

1440 

1506 

1572 

1639 

1706 

21 

870 

932 

995 

57 

20 

84 

48 

12 

76 

41 

07 

73 

40 

07 

22 

871 

933 

996 

58 

21 

85 

49 

13 

77 

43 

08 

74 

41 

08 

23 

872 

934 

997 

59 

22 

86 

50 

14 

79 

44 

09 

75 

42 

09 

24 

873 

935 

998 

60 

23 

87 

51 

15 

80 

45 

10 

77 

43 

11 

25 

874 

936 

999 

61 

25 

88 

52 

16 

81 

46 

11 

78 

44 

12 

26 

875 

937 

1000 

63 

26 

89 

53 

17 

82 

47 

13 

79 

45 

13 

2 ? 

876 

938 

1001 

64 

27 

90 

54 

18 

83 

48 

14 

80 

47 

14 

28 

877 

939 

1002 

65 

28 

91 

55 

19 

84 

49 

15 

81 

48 

15 

29 

878 

941 

1003 

66 

29 

92 

56 

20 

85 

50 

16 

82 

49 

16 

30 

879 

942 

1004 

1067 

1130 

1193 

1257 

1321 

1386 

1451 

1517 

1583 

1650 

1717 

31 

880 

943 

05 

68 

31 

94 

58 

22 

87 

52 

18 

84 

51 

18 

32 

882 

944 

08 

69 

32 

95 

59 

24 

88 

53 

19 

85 

52 

20 

33 

883 

945 

07 

70 

33 

96 

60 

25 

89 

55 

20 

86 

53 

21 

34 

884 

946 

08 

71 

34 

98 

61 

26 

90 

56 

21 

88 

54 

22 

35 

885 

947 

09 

72 

35 

99 

62 

27 

92 

57 

22 

89 

56 

23 

36 

886 

948 

10 

73 

36 

1200 

64 

28 

93 

58 

24 

90 

57 

24 

37 

887 

949 

11 

74 

37 

01 

65 

29 

94 

59 

25 

91 

58 

25 

38 

888 

950 

12 

75 

38 

02 

66 

30 

95 

GO 

26 

92 

59 

26 

39 

889 

951 

13 

76 

39 

03 

67 

31 

96 

61 

27 

93 

60 

27 

40 

890 

952 

1014 

1077 

1140 

1204 

1268 

1332 

1397 

1462 

1528 

1594 

1661 

1729 

41 

891 

953 

15 

78 

41 

05 

69 

33 

98 

63 

29 

96 

62 

30 

42 

892 

954 

16 

79 

42 

08 

70 

34 

99 

64 

30 

97 

63 

31 

43 

893 

955 

18 

80 

44 

07 

■71 

35 

1400 

65 

31 

98 

64 

32 

44 

894 

956 

19 

81 

45 

08 

72 

36 

01 

67 

* 32 

99 

66 

33 

45 

895 

957 

20 

82 

46 

09 

73 

38 

02 

68 

33 

1600 

67 

34 

46 

896 

958 

21 

84 

47 

10 

74 

39 

03 

69 

35 

01 

68 

35 

4-7 

897 

959 

22 

85 

48 

11 

75 

40 

05 

70 

36 

02 

69 

36 

48 

898 

960 

23 

86 

49 

12 

76 

41 

06 

71 

37 

03 

70 

38 

49 

899 

961 

24 

87 

50 

13 

77 

42 

07 

72 

38 

04 

71 

39 

50 

900 

962 

1#25 

1088 

1151 

1215 

1278 

1343 

1408 

1473 

1539 

1605 

1672 

1740 

51 

901 

963 

26 

89 

52 

16 

80 

44 

09 

74 

40 

0 G 

73 

41 

52 

902 

964 

27 

90 

53 

17 

81 

45 

10 

75 

41 

08 

75 

42 

53 

903 

965 

28 

91 

54 

18 

82 

46 

11 

76 

42 

09 

76 

43 

54 

904 

966 

29 

92 

55 

19 

83 

47 

12 

77 

43 

10 

77 

44 

55 

905 

968 

30 

93 

56 

20 

84 

48 

13 

79 

44 

11 

78 

46 

56 

906 

969 

31 

94 

57 

21 

85 

49 

14 

80 

46 

12 

79 

47 

57 

907 

970 

32 

95 

58 

22 

86 

50 

15 

81 

47 

13 

80 

48 

58 

908 

971 

33 

96 

59 

23 

87 

52 

16 

82 

48 

14 

81 

49 

59 

909 

972 

34 

97 

60 

24 

88 

53 

18 

83 

49 

15 

82 

50 












































TABLE OF MERIDIONAL PARTS. 


97 


M. | 28Q| 29Q| 3QQ| 31Q| 320| 33o" 3 4Qj 35Q| 36°) 370| 3SOj 390j 400] 410 


0 

1751 

1819 

1888 

1958 

2028 

2100 

2171 

2244 2318 

2393 

2468 

2545 

2623 2702 

1 

52 

21 

90 

59 

30 

01 

73 

46' 

19 

94 

70 

46 

24 

03 

2 

53 

22 

91 

60 

31 

02 

74 

47 

20 

95 

71 

48 

25 

04 

3 

55 

23 

92 

62 

32 

03 

75 

48 

22 

96 

72 

49 

27 

06 

4 

56 

24 

93 

63 

33 

04 

76 

49 

23 

98 

73 

50 

28 

07 

5 

57 

25 

94 

64 

34 

05 

78 

50 

24 

99 

75 

51 

29 

OS 

6 

58 

26 

95 

65 

35 

07 

79 

52 

25 

2400 

76 

53 

31 

10 

7 

59 

27 

96 

66 

37 

08 

80 

53 

27 

01 

77 

54 

32 

11 

8 

60 

29 

98 

67 

38 

09 

81 

54 

28 

03 

78 

55 

33 

12 

9 

61 

30 

99 

69 

39 

10 

82 

55 

29 

04 

80 

57 

34 

14 

10 

1762 

1831 

1900 

1970 

2040 

2111 

2184 

2257 

2330 

2405 

2481 

2558 

2636 

2715 

11 

64 

32 

01 

71 

41 

13 

85 

58 

32 

06 

82 

59 

37 

16 

12 

65 

33 

02 

72 

43 

14 

86 

59 

33 

08 

84 

60 

38 

18 

13 

66 

34 

03 

73 

44 

'15 

87 

60 

34 

09 

85 

62 

40 

19 

14 

67 

35 

05 

74 

45 

16 

88 

61 

35 

10 

86 

63 

41 

20 

15 

68 

37 

06 

76 

46 

17 

90 

63 

37 

11 

87 

64 

42 

22 

16 

69 

38 

07 

77 

47 

19 

91 

64 

38 

13 

89 

66 

44 

23 

17 

70 

39 

08 

78 

48 

20 

92 

65 

39 

14 

90 

67 

45 

24 

18 

72 

40 

09 

79 

50 

21 

93 

66 

40 

15 

91 

68 

46 

26 

19 

73 

41 

10 

80 

51 

22 

94 

68 

42 

16 

92 

69 

48 

27 

20 

1774 

1842 

1912 

1981 

2052 

2123 

2196 

2269 

2343 

2418 

2494 

2571 

2649 

2728 

21 

75 

43 

13 

83 

53 

25 

97 

70 

44 

19 

95 

72 

50 

29 

22 

76 

45 

14 

84 

54 

26 

98 

71 

45 

20 

96 

73 

51 

31 

23 

77 

46 

15 

85 

56 

27 

99 

72 

46 

22 

98 

75 

53 

32 

24 

78 

47 

16 

86 

57 

28 

2200 

74 

48 

23 

99 

76 

54 

33 

25 

80 

48 

17 

87 

58 

29 

02 

75 

49 

24 

2500 

77 

55 

35 

26 

81 

49 

18 

88 

59 

31 

03 

76 

50 

25 

01 

78 

57 

36 

27 

82 

50 

20 

90 

60 

32 

04 

77 

51 

27 

03 

80 

58 

37 

28 

83 

52 

21 

91 

61 

33 

05 

79 

53 

28 

04 

81 

59 

39 

29 

84 

53 

22 

92 

63 

34 

07 

80 

54 

29 

05 

82 

61 

40 

30 

1785 

1854 

1923 

1993 

2064 

2135 

2208 

2281 

2355 

2430 

2506 

2584 

2662 

2742 

31 

86 

55 

24 

94 

65 

37 

09 

82 

56 

32 

08 

85 

63 

43 

32 

87 

56 

25 

95 

66 

38 

10 

83 

58 

33 

09 

86 

65 

44* 

33 

89 

57 

27 

97 

67 

39 

11 

85 

59 

34 

10 

88 

66 

46 

34 

90 

58 

28 

98 

69 

40 

13 

86 

60 

35 

12 

89 

67 

47 

35 

91 

60 

29 

99 

70 

41 

14 

87 

61 

37 

13 

90 

69 

48 

36 

92 

61 

30 

2000 

71 

43 

15 

88 

63 

38 

14 

91 

70 

50 

37 

93 

62 

31 

01 

72 

44 

16 

90 

64 

39 

15 

93 

71 

51 

38 

94 

63 

32 

02 

73 

45 

17 

91 

65 

40 

17 

94 

73 

52 

39 

95 

64 

34 

04 

75 

46 

19 

92 

66 

42 

18 

95 

74 

54 

40 

1797* 

1865 

1935 

2005 

2076 

2147 

2220 

2293 

2368 

2443 

2519 

2597 

2675 

2755 

41 

98 

06 

36 

06 

77 

49 

21 

95 

69 

44 

21 

98 

76 

56 

42 

99 

68 

37 

07 

78 

50 

22 

96 

70 

45 

22 

99 

78 

58 

43 

1800 

69 

38 

08 

79 

51 

24 

97 

71 

47 

23 

2600 

79 

59 

44 

01 

70 

39 

10 

80 

52 

25 

98 

73 

48 

24 

02 

80 

00 

45 

02 

71 

41 

11 

82 

53 

26 

99 

74 

49 

26 

03 

82 

62 

46 

03 

72 

42 

12 

83 

55 

27 

2301 

75 

51 

27 

04 

83 

63 

47 

05 

73 

43 

-13 

84 

56 

28 

02 

76 

52 

28 

06 

84 

64 

48 

06 

75 

44 

14 

85 

57 

30 

03 

78 

53 

30 

07 

86 

66 

49 

07 

76 

45 

15 

86 

58 

31 

04 

79 

54 

31 

08 

87 

67 

50 

1808 

1877 

1946 

2017 

2088 

2159 

2232 

2306 

2380 

2456 

2532 

2010 

2688 

2768 

51 

09 

78 

48 

18 

89 

61 

33 

07 

81 

57 

33 

11 

90 

70 

52 

10 

79 

49 

19 

90 

62 

35 

08 

83 

58 

35 

12 

91 

71 

53 

11 

80 

50 

20 

91 

63 

36 

09 

84 

59 

36 

14 

92 

72 

54 

13 

81 

51 

21 

92 

64 

37 

11 

85 

61 

37 

15 

94 

74 

55 

14 

83 

52 

22 

94 

65 

38 

12 

86 

62 

38 

10 

95 

75 

56 

15 

84 

53 

24 

95 

67 

39 

13 

88 

63 

40 

17 

96 

76 

57 

16 

85 

55 

25 

96 

68 

41 

14 

89 

. 64 

41 

19 

9S 

78 

58 

17 

S6 

56 

26 

97 

69 

42 

16 

90 

66 

42 

20 

99 

79 

59 

18 

87 

67 

27 

98 

70 

43 

1 IT 

91 

67 

441 21 

2701 

80 















































98 TABLE OF MERIDIONAL PARTS. 


M. 

| 420 

430 

4401 

4501 4601 4701 48°| 

jo 

50°| 510, 520) 

5301 

540 

550 

0 

2782,2863 

2946 

3030 

3116 

3203|3292|3382 

3474 

3569 

3665 

3764 

3865 

3968 

] 

83 

64 

47 

31 

17 

04! 93 

84 

76 

70 

67 

65 

67 

70 

2 

84 

66 

49 

33 

18 

06 

So 

85 

78 

72 

68 

67 

68 

71 

3 

88 

67 

50 

34 

20 

07 

96 

87 

79 

74 

70 

69 

70 

73 

4 

87 

69 

51 

36 

21 

09 

98 

88 

81 

75 

72 

70 

71 

75 

5 

88 

70 

53 

37 

23 

10 

99 

90 

82 

77 

73 

72 

73 

77 

6 

90 

71 

54 

38 

24 

12 

3301 

91 

84 

78 

75 

74 

75 

78 

7 

91 

73 

56 

40 

26 

13 

02 

93 

85 

80 

77 

75 

77 

80 

8 

92 

74 

57 

• 41 

27 

14 

03 

94 

87 

82 

78 

77 

78 

82 

9 

94 

75 

58 

43 

29 

16 

05 

96 

88 

83 

80 

79 

SO 

84 

10 

2795 

2877 

2930 

3044 

3130 

3217 

3306 

3397 

3490 

3585 

3381 

3780 

3882 

3985 

11 

97 

78 

61 

46 

31 

19 

OS 

99 

92 

86 

83 

82 

S3 

87 

12 

98 

80 

63 

47 

33 

20 

09 

3400 

93 

88 

85 

84 

85 

89 

13 

99 

81 

64 

48 

34 

22 

11 

02 

95 

90 

86 

85 

87 

91 

14 

2801 

82 

65 

50 

36 

23 

12 

03 

96 

91 

88 

87 

89 

92 

] 5 

02 

84 

67 

51 

37 

25 

14 

05 

98 

93 

90 

89 

90 

94 

16 

03 

85 

68 

53 

39 

26 

16 

07 

99 

94 

91 

90 

92 

96 

17 

05 

86 

70 

54 

40 

28 

17 

08 

3501 

93 

93 

92 

94 

98 

18 

08 

88 

71 

55 

42 

29 

19 

10 

03 

93 

95 

94 

95 

99 

19 

07 

89 

72 

57 

43 

31 

20 

11 

04 

99 

96 

95 

97 

4001 

20 

2809 

2891 

2974 

3058 

3144 

3232 

3322 

3413 

3506 

3601 

3398 

3797 

3899 

4003 

21 

10 

92 

75 

60 

46 

34 

24 

14 

07 

02 

99 

99 

3991 

05 

22 

11 

93 

76 

61 

47 

35 

25 

16 

09 

04 

3701 

3800 

02 

06 

23 

13 

95 

78 

63 

49 

37 

26 

17 

10 

06 

03 

02 

04 

08 

21 

14 

96 

79 

64 

50 

38 

28 

19 

12 

07 

04 

04 

06 

10 

25 

15 

97 

81 

65 

52 

40 

29 

20 

14 

09 

06 

06 

07 

12 

2 G 

17 

99 

82 

67 

53 

41 

31 

22 

15 

10 

07 

07 

09 

14 

27 

18 

2900 

83 

68 

55 

42 

OO 

04 

23 

17 

12 

09 

09 

11 

15 

28 

20 

02 

85 

70 

56 

44 

34 

25 

18 

14 

11 

11 

13 

17 

29 

21 

03 

86 

71 

57 

45 

35 

27 

20 

15 

13 

12 

14 

19 

30 

2822 

2904 

2988 

3073 

3159 

3247 

3337 

3428 

3521 

3617 

3714 

3314 

3916 

4021 

31 

24 

06 

89 

74 

60 

48 

38 

30 

23 

18 

16 

16 

18 

22 

32 

25 

07 

91 

75 

62 

50 

40 

31 

25 

20 

17 

17 

19 

24 

33 

26 

08 

92 

77 

63 

51 

41 

33 

26 

22 

19 

19 

21 

26 

34 

28 

10 

93 

78 

65 

53 

43 

34 

28 

23 

21 

21 

22 

28 

35 

29 

11 

95 

80 

66 

54 

44 

36 

29 

25 

22 

OO 

25 

29 

3G 

30 

13 

96 

81 

68 

56 

46 

37 

31 

26 

24 

24 

26 

31 

37 

32 

14 

98 

83 

69 

57 

47 

39 

32 

28 

26 

26 

28 

33 

38 

33 

15 

99 

84 

71 

59 

49 

40 

34 

30 

27 

27 

30 

35 

39 

34 

17 

3000 

85 

72 

60 

50 

42 

36 

31 

29 

29 

. 32 

37 

40 

2836 

2918 

3002 

3087 

3173 

3262 

3352 

3443 

3537 

3633 

3731 

3331 

3933 

4038 

41 

37 

19 

03 

88 

75 

63 

53 

45 

39 

34 

32 

32 

35 

40 

42 

39 

21 

05 

90 

76 

65 

55 

47 

40 

36 

34 

34 

37 

42 

43 

40 

22 

06 

91 

78 

66 

56 

48 

42 

38 

30 

36 

38 

44 

44 

41 

24 

07 

93 

79 

68 

58 

50 

43 

39 

37 

38 

40 

45 

45 

43 

25 

09 

94 

81 

69 

59 

51 

45 

41 

39 

39 

42 

47 

46 

44 

26 

10 

95 

82 

71 

61 

53 

47 

43 

41 

41 

44 

49 

47 

45 

28 

12 

97 

84 

72 

62 

54 

48 

44 

42 

43 

45 

51 

48 

47 

29 

13 

98 

85 

74 

64 

56 

50 

46 

44 

44 

47 

52 

49 

48 

31 

14 

3100 

87 

75 

65 

57 

51 

47 

46 

46 

49 

54 

50 

2849 

2932 

3016 

3101 

3188 

3277 

3367 

3459 

3553 

3649 

3747 

3848 

3951 

4056 

51 

51 

33 

17 

03 

90 

78 

68 

60 

55 

51 

49 

49 

52 

58 

52 

52 

35 

19 

04 

91 

80 

70 

62 

56 

52 

50 

51 

54 

00 

53 

54 

36 

20 

05 

92 

81 

71 

64 

58 

54 

52 

53 

56 

61 

54 

55 

37 

21 

07 

94 

83 

73 

65 

59 

55 

54 

54 

58 

63 

55 

56 

39 

23 

08 

95 

84 

74 

67 

61 

57 

55 

5G 

59 

65 

56 

58 

40 

24 

10 

97 

86 

76 

68 

62 

59 

57 

58 

61 

67 

57 

59 

42 

26 

11 

98 

87 

78 

70 

64 

' 60 

59 

60 

63 

69 

58 

60 

43 

27 

13 

3200 

89 

79 

71 

66 

62 

60 

61 

64 

70 

59 

62 

44 

29 

14 

01 

901 81 

731 67 

64 

62 

63 

66 

72 








































TABLE OP MERIDIONAL PARTS. 09 


Vi. | 5uQ|" "570j 58Q1 5Qo|' GQoj" G1 Q| 02Q[ G3Q| G4Q| G5o| GGO| G70| GS^| G'jo 


0 4074 

4183 

4294 

4409 

4527 

4649 

477514905 

5039 5179 

5324 

5474,5631 

5795 

1 

76 

84 

96 

11 

29 

51 

77 

07 

42 

81 

26 

77 

33 

97 

2 

77 

86 

98 

13 

31 

53 

79 

09 

44 

84 

28 

79 

36 5800 

3 

79 

88 

4300 

15 

33 

55 

81 

12 

46 

86 

31 

82 

39 

03 

4 

81 

90 

02 

17 

35 

57 

84 

14 

49 

88 

33 

84 

42 

06 

5 

83 

92 

04 

19 

37 

60 

86 

18 

K. 1 

X 

91 

36 

87 

44 

09 

G 

85 

94 

06 

21 

39 

62 

88 

18 

53 

93 

38 

89 

47 

11 

7 

86 

95 

08 

23 

41 

64 

90 

20 

55 

95 

41 

92 

50 

14 

8 

88 

97 

09 

25 

43 

66 

92 

23 

58 

98 

43 

95 

52 

17 

9 

90 

99 

11 

27 

45 

68 

94 

25 

60 5200 

46 

97 

55 

20 

10 4092 

4201 

4313 

4429 

4547 

4670 

4796 

4927 

5062 5203 

5348 

5500 

5658 

5823 

11 

94 

03 

15 

31 

49 

72 

98 

29 

65 

05 

51 

02 

60 

25 

12 

95 

05 

17 

33 

51 

74 

4S01 

31 

67 

07 

53 

05 

63 

28 

13 

97 

07 

19 

34 

53 

76 

03 

34 

69 

10 

56 

07 

66 

31 

14 

99 

08 

21 

36 

55 

78 

05 

36 

71 

12 

58 

10 

6 S 

34 

15 4101 

10 

23 

38 

57 

80 

07 

38 

74 

14 

61 

13 

71 

37 

1G 

03 

12 

25 

40 

59 

82 

09 

40 

76 

17 

63 

15 

74 

39 

17 

04 

14 

27 

42 

62 

84 

11 

43 

78 

19 

66 

18 

76 

42 

IS 

0 G 

16 

28 

44 

64 

87 

14 

45 

81 

22 

68 

20 

79 

45 

19 

08 

18 

30 

46 

66 

89 

16 

47 

83 

24 

71 

23 

82 

48 

20 

4110 

4220 

4332 

4448 

4568 

4691 

4818 

4949 

5085 

5226 

5373 

5526 

5685 

5851 

21 

12 

21 

34 

50 

70 

93 

20 

51 

88 

29 

76 

28 

87 

54 

22 

13 

23 

36 

52 

72 

95 

22 

54 

90 

31 

78 

31 

90 

56 

23 

15 

25 

38 

54 

74 

97 

24 

56 

92 

34 

80 

33 

93 

59 

24 

17 

27 

40 

56 

76 

99 

26 

58 

95 

36 

83 

36 

95 

62 

25 

19 

29 

42 

58 

78 

4701 

29 

60 

97 

38 

85 

39 

98 

65 

2G 

21 

31 

44 

60 

80 

03 

31 

63 

99 

41 

88 

41 

5701 

68 

27 

22 

32 

46 

62 

82 

05 

33 

65 

5102 

43 

90 

44 

04 

71 

28 

24 

34 

47 

64 

84 

07 

35 

67 

04 

46 

93 

46 

08 

74 

29 

26 

36 

49 

66 

86 

10 

37 

69 

06 

48 

95 

49 

09 

76 

30 

4128 

4233 

4351 

4468 

4588 

4712 

4839 

4972 

5108 

5250 

5398 

5552 

5712 

5879 

31 

30 

40 

53 

70 

90 

14 

42 

74 

11 

53 

5401 

54 

15 

82 

32 

32 

42 

55 

72 

92 

16 

44 

76 

13 

55 

03 

57 

17 

85 

33 

33 

44 

57 

74 

94 

18 

46 

78 

15 

58 

06 

59 

20 

88 

34 

35 

46 

59 

76 

96 

20 

48 

81 

18 

60 

OS 

62 

23 

91 

35 

37 

47 

61 

78 

98 

22 

50 

83 

20 

63 

11 

65 

25 

94 

3G 

39 

49 

63 

80 

4600 

24 

52 

85 

22 

65 

13 

67 

28 

96 

37 

41 

51 

65 

82 

02 

26 

55 

87 

25 

67 

16 

70 

31 

99 

38 

42 

53 

67 

84 

04 

28 

57 

90 

27 

70 

18 

73 

34 

5902 

39 

44- 

55 

69 

86 

06 

31 

59 

92 

29 

72 

21 

75 

36 

05 

40 

4146 

4257 

4370 

4488 

4608 

4733 

4861 

<$994 

5132 

5275 

5423 

5578 

5739 

5908 

41 

48 

59 

72 

90 

10 

35 

63 

98 

34 

77 

26 

80 

42 

11 

42 

50 

60 

74 

92 

12 

37 

65 

99 

36 

80 

28 

83 

45 

14 

43 

52 

62 

76 

94 

14 

39 

68 

5001 

39 

82 

31 

86 

47 

17 

44 

53 

64 

78 

95 

16 

41 

70 

03 

41 

84 

33 

88 

50 

19 

45 

55 

66 

80 

97 

18 

43 

72 

05 

43 

87 

36 

91 

53 

22 

46 

57 

68 

82 

99 

20 

45 

74 

08 

46 

89 

38 

94 

56 

25 

47 

59 

70 

84 

4501 

23 

47 

76 

10 

48 

92 

41 

96 

58 

28 

48 

61 

72 

86 

03 

25 

50 

79 

12 

51 

94 

43 

99 

61 

31 

49 

G2 

74 

88 

05 

27 

52 

81 

14 

53 

97 

46 

5602 

64 

34 

50 

1164 

4275 

4390 

4507 

4629 

4754 

4883 

5017 

5155 

5299 

5448 

5604 

5767 

5937 

51 

66 

77 

92 

09 

31 

56 

85 

19 

58 

5301 

51 

07 

70 

40 

52 

6 S 

79 

94 

11 

33 

58 

87 

21 

60 

04 

54 

10 

72 

43 

53 

70 

81 

96 

13 

35 

60 

90 

23 

62 

06 

56 

12 

75 

4G 

54 

72 

83 

98 

15 

37 

62 

92 

26 

65 

09 

59 

15 

78 

48 

55 

73 

85 

99 

17 

39 

64 

94 

28 

67 

11 

61 

17 

81 

51 

5G 

75 

87 

4401 

19 

41 

66 

96 

30 

69 

14 

64 

20 

83 

54 

57 

77 

89 

03 

21 

43 

69 

98 

33 

72 

16 

66 

23 

86 

57 

58 

79 

91 

05 

23 

45 

71 

4901 

35 

74 

19 

69 

25 

89 

60 

59 

81 

92 

07 

25 

47 

73 

03 

37 

76 

21 

71 

28 

92 

63 









































100 


TABLE OF MERIDIONAL PARTS. 


M.| ~ Tio] 72°| 73°| 74-Oj 75Q| 76Q| 77°) 7SO| 79o| 80O| 81Q| 82Q| 830 


' 0 

5906 6146 

6335 

6534 

6746 

6970 

7210 

7467 

7745 

8046 

8375 

8739 9145 

9605 

1 

69 

49 

38 

38 

49 

74 

14 

72 

49 

51 

81 

45 

53 

14 

o 

72 

52 

41 

41 

53 

78 

18 

76 

54 

56 

87 

52 

60 

22 

3 

75 

55 

45 

45 

57 

82 

22 

81 

59 

61 

93 

58 

67 

31 

4 

78 

58 

48 

48 

60 

86 

27 

85 

64 

67 

98 

65 

74 

39 

5 

81 

61 

51 

52 

64 

90 

31 

80 

69 

72 

8404 

71 

82 

47 

6 

84 

64 

54 

55 

68 

94 

35 

94 

74 

77 

10 

78 

89 

55 

7 

' 86 

67 

58 

58 

71 

97 

39 

98 

78 

83 

16 

84 

96 

64 

8 

89 

70 

61 

62 

75 

7001 

43 

7503 

83 

88 

22 

91 

9203 

72 

9 

no 

73 

64 

65 

79 

05 

47 

07 

88 

93 

27 

97 

11 

81 

10 

5995 

6177 

6367 

0569 

6782 

7009 

7252 

7512 

7793 

8099 

8433 

S804 

9218 

9689 

11 

98 

80 

71 

72 

86 

13 

56 

16 

98 

8104 

39 

10 

25 

97 

12 

6001 

83 

74 

76 

90 

17 

60 

21 

7803 

09 

45 

17 

33 

9706 

13 

04 

86 

77 

79 

93 

21 

64 

25 

08 

15 

51 

23 

40 

14 

14 

07 

89 

80 

83 

97 

25 

68 

30 

13 

20 

57 

30 

48 

23 

15 

10 

92 

84 

86 

6801 

29 

73 

35 

17 

25 

63 

36 

55 

31 

16 

13 

95 

87 

90 

04 

33 

77 

39 

22 

31 

69 

43 

62 

40 

17 

16 

98 

90 

93 

08 

37 

81 

44 

27 

36 

74 

49 

70 

48 

18 

19 

6201 

94 

96 

12 

41 

85 

48 

32 

41 

80 

56 

77 

57 

19 

22 

05 

97 

6600 

15 

45 

89 

53 

37 

47 

86 

63 

85 

65 

20 

6025 

6208 

6400 

6603 

6819 

7049 

7294 

7557 

7842 

8152 

8492 

8869 

9292 

9774 

21 

28 

11 

03 

07 

23 

52 

98 

02 

47 

58 

98 

76 

9300 

83 

22 

31 

. 14 

07 

10 

26 

56 

7302 

66 

52 

63 

8504 

83 

07 

91 

23 

34 

17 

10 

14 

30 

GO 

06 

71 

57 

68 

10 

89 

15 

9800 

24 

37 

20 

13 

17 

34 

64 

11 

76 

62 

74 

16 

96 

22 

09 

25 

40 

23 

17 

21 

38 

68 

15 

80 

67 

79 

22 

8903 

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